Re: AI-GEOSTATS: RES: Tomorrow: Webinar: April 28th, Applied Example of Data Science Technology
Is it just me or does this advert say Monday 28th April??
http://www.kriging.com/whereisshe.htm
From: Marcus Mattos Riether marcus.riet...@caixaseguros.com.br
To: Lisa Solomon li...@salford-systems.com; ai-geostats@jrc.it
ai-geostats@jrc.it
Sent: Tuesday, April 28, 2015 11:43 AM
Subject: AI-GEOSTATS: RES: Tomorrow: Webinar: April 28th, Applied Example of
Data Science Technology
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{margin-bottom:0cm;}#yiv7785629914 ul {margin-bottom:0cm;}#yiv7785629914 Dear
Lisa, I had already filled-up my agenda for today at the time of seminar. I
would be very happy if you could send me a recording. Best regards,
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| | Marcus M Riether
Gerente de Resseguro
Gerência de Resseguro - GERSEG
Diretoria Técnica e de Controle de Riscos - DIRAT
Tel + 55 61 2192 2759 |
De: gregoire.dub...@gmail.com [mailto:gregoire.dub...@gmail.com]Em nome de Lisa
Solomon
Enviada em: segunda-feira, 27 de abril de 2015 16:52
Para: ai-geostats@jrc.it
Assunto: AI-GEOSTATS: Tomorrow: Webinar: April 28th, Applied Example of Data
Science Technology Webinar: Monday, April 28th This webinar will be a
step-by-step presentation that you can repeat on yourown geo, spatial AND
APPLIED datasets!Although the focus is ROI and Business,corresponding GEO and
SpatialApplications include: scenario planning, risk
AI-GEOSTATS: Journals
Aargh! Stop stop. They are gone! I have a waiting list of 10 for my IAMG and CG and am getting repetitive strain injury from typing apologies. If anyone else out there wants to clear their libraries or studies, please let me know. I would be more than happy to co-ordinate a clearing house between wants and haves. Happy New Year to everyone Isobel Clark Do You Yahoo!? Get your free @yahoo.co.uk address at http://mail.yahoo.co.uk or your free @yahoo.ie address at http://mail.yahoo.ie -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and "unsubscribe ai-geostats" followed by "end" on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: spatial statistics for small data sets
Dear Raechel The answer to your question is a bit chicken-and-egg-ish. If your data is well behaved (simple distribution, pretty continuous) then you can get meaningful results from very few samples (probably not less than 20 or so!!) We have examples in the book with data sets of 27 and up. The 27 one is no good for geostatistics but this has more to do with the fact that the samples are 1km apart when the range of influence is probably about 125 metres. The main tutorial set in the old book (available free at http://uk.geocities.com/drisobelclark/practica.html) which we now call "Page 95" has 50 samples very inefficiently placed which still yield good results for interpretation and estimation purposes. Even more so for simulation basis. So, I would say, go ahead and try it but look at your distribution before you go to geostatistics. Small data sets will give much better results if Normal (Gaussian) or normalised or transformed in some other way. If I can be of any more help, please let me know Isobel Clark Do You Yahoo!? Get your free @yahoo.co.uk address at http://mail.yahoo.co.uk or your free @yahoo.ie address at http://mail.yahoo.ie -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and "unsubscribe ai-geostats" followed by "end" on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: Block size - estimation variance - resource category.
--- William Thayer [EMAIL PROTECTED] wrote: Isobel: Would you mind expanding a little on your earlier reply? In particular, what do you mean by (1) "kriging variance less than ordinary statistical sample variance", (2) "not measured but within the range of influence of at least 4 samples" and (3) "indicated is within range but the local average is a better estimator than the kriging"? Thanks in advance, Bill Hi Bill It is possible for the kriging variance to be higher than the total sill of the semi-variogram. This total sill is (theoretically) equal to the Normal population variance if your data is (a) stationary and (b) Normal. For lognormals use logarithms. Or transform data to Normal scores before calculating semi-variogram. For example: if you estimate a point location from a single sample just below the range of influence away, the kriging variance is twice the total sill (unless you follow the Stanford school, in which case it is twice the total sill minus twice the nugget effect). Now, if the kriging variance is higher than the 'sample' variance, it means that the population mean (if you knew it) would be a better estimator than the local kriging estimate. So even if you have samples within the range of influence, you could still get an estimate which has worse confidence than the regional average. This I call "indicated". I'm sure it is there but I can't put a local value on it. If the kriging variance is less than the total sill (suitably modified for non-point support), then one can assign a 'local' value which is better than the regional average. I consider this "measured". Anything outside the range of influence is speculative and the province of the geologist. I am a mining engineer and don't do "inferred". Does this help? Isobel http://uk.geocities.com/drisobelclark PS: I have fond memories of Syracuse. Spent the summer of '76 as visiting prof in geology. Do You Yahoo!? Get your free @yahoo.co.uk address at http://mail.yahoo.co.uk or your free @yahoo.ie address at http://mail.yahoo.ie -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and "unsubscribe ai-geostats" followed by "end" on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: Variowin equations and cross-validation
Juliann Judging the fit of a model cannot be done from the summary statisics. See my 1986 paper "The Art of Cross Validation" (full reference at http://uk.geocities.com/drisobelclark/Publications.html) Better to use something like Noel Cressie's goodness of fit statistic which tests the semi-variogram fit to the experimental with a weighted least squares. Isobel Clark Do You Yahoo!? Get your free @yahoo.co.uk address at http://mail.yahoo.co.uk or your free @yahoo.ie address at http://mail.yahoo.ie -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and "unsubscribe ai-geostats" followed by "end" on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: Variowin equations and cross-validation
AAgh, sprry people, Mark Burnett just pointed out that I missed a bit in the Web reference: http://uk.geocities.com/drisobelclark/resume/Publications.html Mea culpa Isobel Clark Do You Yahoo!? Get your free @yahoo.co.uk address at http://mail.yahoo.co.uk or your free @yahoo.ie address at http://mail.yahoo.ie -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and "unsubscribe ai-geostats" followed by "end" on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
AI-GEOSTATS: conferences and courses
Hi all I hope no-one will be offended by this e-mail. Given the recent problems with the main Web site, I hope no-one will mind if I remind you all that sandwiched between: AAPG in Denver 3-6 June 2001 and the SIAM conference in Boulder 11-14 June 2001 we are holding the Zero to Kriging in 30 hours course at the IGWMC in Golden, Colorado 7-10 June 2001. Anyone who registers and turns up the day before is invited to my birthday party on 6th!! Details on the course and all other IGWMC activities can be found at http://www.mines.edu/research/igwmc/short-course/geostat.htm Isobel Clark http://uk.geocities.com/geoecosse/news.html Do You Yahoo!? Get your free @yahoo.co.uk address at http://mail.yahoo.co.uk or your free @yahoo.ie address at http://mail.yahoo.ie -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: Non-Monotone Variogram model
A graph of semivariogram gamma(h) |. | . | . . |.. | .. . |. . . | . .. | . | . |. . . . | . . . |_ h ^ Waghei If this is an omni-directional semi-variogram, then what you have is a severe case of anisotropy probably complicated by a strong trend. I would hazard a guess that you start to runout of pairs of samples in one or more directions somewhere around the ^ above. Try constructing directional semi-variograms and post-plotting the data to identify directional differences. Isobel Clark http://uk.geocities.com/drisobelclark Do You Yahoo!? Get your free @yahoo.co.uk address at http://mail.yahoo.co.uk or your free @yahoo.ie address at http://mail.yahoo.ie -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS:
Ian The use of regression slope to measure kriging efficiency or confidence in an estimate is spurious. The slope of the regression line has nothing to do with the correlation between true value and estimated value and everything to do with whether or not the standard deviations of these two variables are comparable. In effect, it is a measure of conditional bias, not a measure of correlation. In fact, if you are using a least squares regression on Normalised data, with the same units on both variables, the standard deviation of the estimated values would have to be lower than that of the true values to obtain a slope as high as 0.9 -- because least squares is minimising the vertical distance to the line, not the 'true' distance to the line. Better to use the kriging variance for classification needs. For example, you could insist that estimates for (large) blocks of ground lie within a certain confidence percentage of the true value. Companies liek Anglo American use a criteria that the average of the first year's production must be with 15% of the true value at 90% confidence, before they will call it measured. Others companies (such as Iskor) use what we call the ygiagam criterion: Measured: where kriging variance is less than original sample variance (total sill) less within block variance. That is, an estimate can be placed on teh block with more confidence than simply allocating a regional average. Indicated: within the range of influence of at least four boreholes. Inferred: anything the geologist thinks is there. Hope this helps. Isobel Clark http://uk.geocities.com/drisobelclark Do You Yahoo!? Get your free @yahoo.co.uk address at http://mail.yahoo.co.uk or your free @yahoo.ie address at http://mail.yahoo.ie -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: The Estimation of Range paramter is very very big
Are you using some kind of automated fitting? The results would suggest that the model is inappropriate or that your basic assumptions are inappropriate. You should look at how the models are being fitted and what assumptions are made and question everything. Isobel Clark Do You Yahoo!? Get your free @yahoo.co.uk address at http://mail.yahoo.co.uk or your free @yahoo.ie address at http://mail.yahoo.ie -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: Choosing Lag Distance and Angular Tolerance
Andrew You can apply 'standard' geostatistics if the measurements are the 'average' (or some similar feature) over an area. It makes interpeting the semi-variogram extremely tricky if you combine many different sizes of sample, but common sense is the main thing here. The trick is to derive a point semi-variogram model from which any size can be derived (see Chapter 3, Practical Geostatistics 1979, downloadable free from Web, http://uk.geocities.com/drisobelclark/practica.html) Kriging is modified to reflect that the samples are averages, mainly by changing the diagonal elements in the equations so that they are non-zero. I don't know any software package (off hand ) that does this, though. Isobel Clark --- Andrew Mullens [EMAIL PROTECTED] wrote: I have a question relating to this question, certainly not to question the previous writer, it just seems like a good time to bring it up. Will variograming and other such techniques work for the data the previous writer described, e.g samples aren't at points, but areas (and areas that might have very little to do with the question). If they did use points in the calculations where would the points be placed, at the center of the county, at the major population center, at some arbitrary point (e.g most northerly point). I may be miss reading the description, perhaps the sample are point samples, but were taken with one sample in each county. Obviously the point samples are never really point sample, they must be taken over some area, approximating a point, but does this design seem to push the boundaries on that assumption. Andrew - Original Message - From: Yadollah Waghei [EMAIL PROTECTED] To: [EMAIL PROTECTED] Cc: [EMAIL PROTECTED]; [EMAIL PROTECTED]; [EMAIL PROTECTED]; [EMAIL PROTECTED]; [EMAIL PROTECTED]; [EMAIL PROTECTED] Sent: Tuesday, May 15, 2001 7:33 AM Subject: AI-GEOSTATS: Choosing Lag Distance and Angular Tolerance Hello dears I have a spatial data set contaning n=262 observarion (The variable of interest is Rate of Tuberculosis in 262 counties of Iran). I want to fit some models to Directional semi-variograms,and then build anisotropic semi-variogram. Then questions are - Is there any rule for choosing Lag Distance and Angular Tolerance? -Also,how we can balance between Lag Distance and Angular Tolerance? -Do you agree that both must be very small,as possible?(Such that number of pairs in each lag20, for example) Thank you Yadollah Waghei Dep.of Biostatistics Tarbiat Modarres Univ.(Tehran)Po.Box: 14115-111 Tel:8011001-3872 Fax:8007989 ___ Visit http://www.visto.com/info, your free web-based communications center. Visto.com. Life on the Dot. -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org Do You Yahoo!? Get your free @yahoo.co.uk address at http://mail.yahoo.co.uk or your free @yahoo.ie address at http://mail.yahoo.ie -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: Number of data points Variograms
My research is on heavy metal pollution in water bodies. Hi, some thoughts (your numbering): (1) One of the things I have found successful is the following: construct your semi-variogram using ALL of your data but not allowing pairs between samples in different water bodies; use cross validation on each water body separately to see if the 'generic' model works for all of them or whether some are more variable or harder to predict than others; use the generic model for kriging with a variance/sill scaled for each water body. Is there any consistent tested way to approach such 'not-enough-data' situations? Not really, but I have found this works if the 'deposition' is similar in the various bodies. (2) 'Hot spots' are (a) erratic highs due to distribution being skewed or (b) true outliers (inhomogeneities). Which? Tackle accordingly. Cross validation will pick up outliers but not work properly if data is severely skewed. Could it be possible to effectively fit variograms, when the hot spots are present? Try calculating semi-variograms with and without 'hot spots' and see what happens. Kriging is based on an assumption of homogeneity and it is a little unfair to expect it to come back and say that's a daft thing to do ;-) [ For most of the cases I tried with such suspected hotspot data, my results show that the linear interpolation works better than the krigged distribution based on the 'fitted' variograms] I find this statement interesting. How do you define better -- prettier? nicer? easier to interpret? less polluted? Isobel Clark Do You Yahoo!? Get your free @yahoo.co.uk address at http://mail.yahoo.co.uk or your free @yahoo.ie address at http://mail.yahoo.ie -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS:
Maybe I am being really dumb here, but why would you bother to use a covariance function for an unbounded semi-variogram? Why not just use the semi-variogram form of kriging. I always thought that was the whole point of using semi-variograms instead of covariances -- because they were more widely applicable. Is it a software limitation for the package mentioned? Isobel Clark Do You Yahoo!? Get your free @yahoo.co.uk address at http://mail.yahoo.co.uk or your free @yahoo.ie address at http://mail.yahoo.ie -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS:
It is well known that when inverting a matrix it is much better (for numerical reasons) that the higher values are on the diagonal and the lower values far off the diagonal. Have you not heard of pivoting? The computational problems of using a matrix based on the semi-variogram rather than the covariance are removed totally by putting the last equation first in the matrix. Of course, this means you cannot use a computational algorithm which demands a symmetric matrix, but so what? Alternatively, you pivot on the largest term in the first equation, then the second etc. I did a lot of experimentation with this around 15 years ago and found that the two (covariance and semi-variogram) sets of equations become identical after around the second or third 'pivot'. Please let us not confuse programming problems with geostatistical problems. There are a lot of packages out there which ask you to model the semi-variogram and then use a covariance for kriging. There are a lot of packages out there which model the semi-variogram and krige with the semi-variogram. Are there main stream geostatistical (as opposed to statistical or strict GIS) packages which model the covariance? Isobel Clark http://geoecosse.bizland.com Do You Yahoo!? Get your free @yahoo.co.uk address at http://mail.yahoo.co.uk or your free @yahoo.ie address at http://mail.yahoo.ie -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS:
Excuse my persistence, but I think you are missing the point here. If you can produce a covariance function by subtracting the semi-variogram from an arbitrary constant AND if it makes no difference to the resulting equations, you are simply constructing the equations WITH the semi-variogram. Not so? In which case, the necessity to provide a covariance function is an artifact introduced by the way the software package is set up and not a constraint imposed by the kriging method. My original question was whether this is a problem in how the software was written, not a geostatistical problem. Your answer is telling me yes, it is. Thank you. Isobel Do You Yahoo!? Get your free @yahoo.co.uk address at http://mail.yahoo.co.uk or your free @yahoo.ie address at http://mail.yahoo.ie -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS:
Dear Denis I am sorry you think that I am being agressive. I thought I was being quite reasonable, but perception is a subjective thing. I think it is important for readers of this list to understand that there are different ways of coming to the same answer and that there are different opinions between people in that field. I was also under the impression that the purpose of this list is to promote free interchange of information and opinions. I have reached a stage in my life where I realise that other people know much more than I do about many things, including geostatistics. I joined the list -- as I go to conferences and read journals -- to find out what other people have to say and to learn new ways of seeing and doing. Reading back through this thread of discussion, I am reminded of the sort of conversations we have at conferences. A little give-and-take is a valuable thing provided the parties are actually listening to one another and hearing what is said, rather than taking comments personally. You have every right to prefer LU decomposition and I, for one, would never deny it to you. It is certainly more efficient to solve a set of symmetric equations with a method developed for exactly that purpose. What I question is the assertion that it is the most efficient way to tackle the kriging system - especially if it involves introduction of arbitrary constants chosen to ensure a positive covariance. Covariances can be negative and, in the case of an unbounded semi-variogram, presumably should go negative at some point. Since the constant is an artifact and the equations remain mathematically equivalent to using the semi-variogram, my original question remains. Why introduce a complication that is not necessary? Our opinions on this will always differ. It does not matter because we still get the same answers in the end. Surely that is the important fact here? Isobel Clark http://uk.geocities.com/drisobelclark --- Denis ALLARD [EMAIL PROTECTED] wrote: Dear Isobel, Have you not heard of pivoting? I don't understand the point of being so agressive. Of course, you are not the only person in the geostat community who has heard of pivoting. It is standard math stuff for any mathematician/statistician/engineer. But what is also standard math stuff is the well known fact that if you know that your matrix is symetric or def. pos., it is much more efficient to take advantages of the properties of you matrix. So yes, for computational efficiency I prefer to use some sort of LU decomp for which there are much less numerical instabilities if your matrix has the higher values on the diagonal. Now, if you don't believe me, have a look at the numerical receipes for instance. This computational trick is fully transparent for the user, and it must be so. I don't think that any of us confuses geostat and computations. Now, please try to be less agressive in a forum. Not being in full agreement with someone is normal in a scientific community (and in fact in any community), do not take it personaly. In your previous posts, I have seen a couple of assertions that were not completely correct. Since this forum is read by many students, I believe that it is our duty to correct these assertions. Now, please do not take so agressively. It would much more in your honour to acknowledge the corrections. Regards, Denis Allard PS: about your last question, it is of course silly to model the covariance function, and I suspect that you know that very well It is well known that when inverting a matrix it is much better (for numerical reasons) that the higher values are on the diagonal and the lower values far off the diagonal. Have you not heard of pivoting? The computational problems of using a matrix based on the semi-variogram rather than the covariance are removed totally by putting the last equation first in the matrix. Of course, this means you cannot use a computational algorithm which demands a symmetric matrix, but so what? Alternatively, you pivot on the largest term in the first equation, then the second etc. I did a lot of experimentation with this around 15 years ago and found that the two (covariance and semi-variogram) sets of equations become identical after around the second or third 'pivot'. Please let us not confuse programming problems with geostatistical problems. There are a lot of packages out there which ask you to model the semi-variogram and then use a covariance for kriging. There are a lot of packages out there which model the semi-variogram and krige with the semi-variogram. Are there main stream geostatistical (as opposed to statistical or strict GIS) packages which model the covariance? Isobel Clark http://geoecosse.bizland.com Do You Yahoo!? Get your
Re: AI-GEOSTATS: entering the fray
Hi Yetta Jump in, the water is lovely! All contributions equally valid in my e-mail box ;-) I have to confess that I have rarely used an unbounded semi-variogram model. In mining applications, in my experience (which is limited to 30 years in economic mineralisations) semi-variograms which shoot off into the wild blue yonder are usually caused by trend, strong anisotropy or violation of the 'homogeneity' assumptions (stuff like faults etc or skewed distributions). However, the de Wijsian model is extremely popular in Southern Africa and widely used by some major mining houses along with simple kriging. Not my bag, but who am I to judge? There is an interesting paper by Cressie (not got reference to hand, but it must be in his book somewhere) where he treats the Wolfcamp data as an anisotropic generalised linear model. I use a quadratic trend surface and a spherical model for the residuals. The final estimates are almost identical, but the standard errors differ by an order of magnitude. Actually, I used that as an example in a talk in Ireland about 10 days ago. Noel is an archetypical ivory tower academic (and all round good guy), so I guess we did a bit of role reversal there ;-) I agree that the semi-variogram approach is easier for the non-statistician to grasp. Difference in value is a simpler concept to grasp than cross-product, especially when your boss wants to know the likely difference between what you tell him and what really happens! Keep it coming. It is your voices we want to hear, not us border line pensioners Isobel Clark http://uk.geocities.com/drisobelclark Do You Yahoo!? Get your free @yahoo.co.uk address at http://mail.yahoo.co.uk or your free @yahoo.ie address at http://mail.yahoo.ie -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS:
Thank you, Marco! My point exactly. Isobel Do You Yahoo!? Get your free @yahoo.co.uk address at http://mail.yahoo.co.uk or your free @yahoo.ie address at http://mail.yahoo.ie -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: Help
Davide Unless you get software which allows you to code samples by 'individual', the simplest way is to output the calculated semi-variogram for each individual and then use a spreadsheet to combine them, weighted by the number of pairs in each case. Isobel Clark http://geoecosse.bizland.com Do You Yahoo!? Get your free @yahoo.co.uk address at http://mail.yahoo.co.uk or your free @yahoo.ie address at http://mail.yahoo.ie -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: Negative Kriging Weights Estimates
Colin Is my understanding of this compensation correct? Exactly. Why wouldn't the weights for the furtherest samples be calculated by subtracting the weighting of the closer samples from 1, instead of compensating using negative weights afterwards? I am not sure I understand your question. Kriging weights are produced by a set of equations which minimise the variance of the estimation error. All of the weights are determined simultaneously and negative weights can be produced in the solution of the kriging equations. The condition on the weights is that they sum to 1, not that they have to be positive. Negative weights are usually an indication that your data is clustered or that our search radius is larger than it need be. Some packages will eliminate the samples with negative weights and then re-solve the kriging equations without them. Of course, you may have to go round a few times as there is no guarantee that the new set won't have negative weights Isobel Clark http:/uk.geocities.com/drisobelclark Do You Yahoo!? Get your free @yahoo.co.uk address at http://mail.yahoo.co.uk or your free @yahoo.ie address at http://mail.yahoo.ie -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: Samples in a block
1. What is the optimum number of samples in a block of any particular size? Is there any way that I can work out the theoretical number of samples in an e.g. 30x30m block assuming some a priori information (gold deposit, high nugget of e.g. 1.2 e6, pop.var having the same type of magnitude etc) ? This part I can answer on the general mailing list (I think). Use the free unlimited use downloadable Kriging Game to be found on my pages at http://uk.geocities.com/drisobelclark/briefcase.html This package reads Geostokos type files, Geo-EAS type files, CSVs dumped from spreadsheets or you can type in data from the keyboard. Comments and queries to me please. Isobel Clark Do You Yahoo!? Get your free @yahoo.co.uk address at http://mail.yahoo.co.uk or your free @yahoo.ie address at http://mail.yahoo.ie -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: re: sampling
Hi folks Numerous apologies to anyone who downloaded Krigame over the last two days. The file got corrupted and isn't actually kriging!! New version now up. Sorry sorry sorry Isobel Clark PS: on Mark Burnett's sampling thing. In South African gold mining, they have 100 years of back sampling in similar reefs (or parts of reefs). This helps a lot for designing the 'coarse' sampling suggested by Jan Willem and then developing reliable local models. Do You Yahoo!? Get your free @yahoo.co.uk address at http://mail.yahoo.co.uk or your free @yahoo.ie address at http://mail.yahoo.ie -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: Estimating the fixed Sill in the Elliptic Anisotropy
How can we estimate Sill and Range in all directions by supposing that the sill is fixed? It is usual to fit the sill to an omni-directional semi-variogram graph, since that has most pairs on all points. The ranges can then be fitted individually. The alternate is to 'contour' the experimental semi-variograms in many directions and fit one ellipoidal surface to the 'map'. Isobel Do You Yahoo!? Get your free @yahoo.co.uk address at http://mail.yahoo.co.uk or your free @yahoo.ie address at http://mail.yahoo.ie -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: samples with not normal distribution
What does your data look like after you take logarithms? Is it still skewed? If you do a probability plot does it drop off at the lower end? Or at the top? or is it still curved? Or does it have a kink in it? Geostatistics is possible with any or all of the above but the remedy differs according to your answers. Isobel Clark Do You Yahoo!? Get your free @yahoo.co.uk address at http://mail.yahoo.co.uk or your free @yahoo.ie address at http://mail.yahoo.ie -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: Anisotropy with varying Range and Sill
Any basic Geostatistics book will show you models with varying ranges and sills with direction. Except mine. We believe that sill varying with direction is a symptom of deeper problems such as non-stationarity, trend, discontinuities, etc etc. Isobel Clark http://uk.geocities.com/drisobelclark Do You Yahoo!? Get your free @yahoo.co.uk address at http://mail.yahoo.co.uk or your free @yahoo.ie address at http://mail.yahoo.ie -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: Lognormal kriging and Back Transformation
Colin As I already pointed out higher variance = higher lagrangian multiplier so that some of the efect is cancelled out anyway. We (Geostokos) use the following as a filter: ygiagam (proven resource): kriging variance should be less than original sample variance (total sill) less within block variance probable resource: kriging variance should be less than twice the above and at least 4 samples should be used in the estimation These are fairly arbitrary but have proved sound over the last 10-15 years. Isobel http://uk.geocities.com/drisobelclark Do You Yahoo!? Get your free @yahoo.co.uk address at http://mail.yahoo.co.uk or your free @yahoo.ie address at http://mail.yahoo.ie -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: free spatial analysis software for graduate students
This sounds terrific! I may be a little petty here but how come this is accetable but when we talk about our totally freely distributable teaching software, I get my knuckles rapped? Isobel Clark http://uk.geocities.com/drisobelclark --- Dunrie Greiling [EMAIL PROTECTED] wrote: TerraSeer is offering 10 annual licenses of BoundarySeer and ClusterSeer to outstanding graduate research proposals. TerraSeer will award a total of over $12,000 in software in a contest that will identify superlative research proposals in environmental health, according to Nicholas Jacquez, President of TerraSeer. The identification of health-environment relationships from geographic data is recognized as one of the most pressing problems facing environmental epidemiology, medical geography and the environmental sciences. This contest will foster top-quality research by putting state-of-the-art tools in the hands of top-notch researchers. Dr. Geoff Jacquez, TerraSeer's Chief Scientist, is organizing the group that will review the proposals and make the awards. We're drawing on some of the best scientific minds to run the awards process. I expect this contest to identify and support some truly outstanding research projects. Research proposals shall be submitted through the TerraSeer website and will be accepted through October 31, 2001. These projects will be expected to use the software as part of the analysis. Awards of TerraSeer software will be made in November. Stay tuned to TerraScene for the results of the contest and reports on the research. Enter the contest or learn more at: http://www.terraseer.com/news/news_contest.html Learn more about BoundarySeer at: http://www.terraseer.com/boundaryseer.html Learn more about ClusterSeer at: http://www.terraseer.com/clusterseer.html Download your copy of the TerraSeer demo (featuring BoundarySeer and ClusterSeer plus sample analyses): http://www.terraseer.com/demo/terraseer_demo.html Thanks, Dunrie A. Greiling, Ph.D. [EMAIL PROTECTED] -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org Do You Yahoo!? Get your free @yahoo.co.uk address at http://mail.yahoo.co.uk or your free @yahoo.ie address at http://mail.yahoo.ie -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: Negative variances
Kevin There is something badly wrong with your software. With ordinary kriging, it is not possible to get negative variances. With lognormal kriging, it is not possible to get negative varianse or negative estimates unless you are using a large additive constant. Isobel Clark http://uk.geocities.com/drisobelclark --- Kevin Lowe Rfn [EMAIL PROTECTED] wrote: Hi all I have been experimenting with various kriging methods in estimating Witwatersrand gold grades (South Africa) using Datamine software. I found that using lognormal ordinary kriging has resulted in negative variances in some blocks. My question is why does this happen and what is the significance of it? Kevin Lowe e-mail [EMAIL PROTECTED] -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org Nokia Game is on again. Go to http://uk.yahoo.com/nokiagame/ and join the new all media adventure before November 3rd. -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: Declustering
I would like to know what is the declustering, why we used this method and how we proceed to decluster a set of data? If your data is clustered spatially (in location) this may bias any histograms or probability plots which you draw and, therefore, any conclusions you make about what kind of distribution the values come from. For example, in mining projects geologists tend to drill a lot more holes in the good bits than the bad bits. This means that a histogram contains a lot more samples than it should in the higher end. If you try to fit a model to such data, or use a transform or 'anamorphosis' it will not really reflect the values in the whole of the area. Backtransforms will be biassed like the original samples. Declustering is one way to get rid of the bias. There are various ways to decluster but the most common ones revolve around laying a grid of squares over your map area and either (a) selecting one sample per square or (b) averaging all the samples in each square. (b) is not very sensible given what we are trying to do with the data, but is very common (again) in mining. If you use (a) it is a good idea to choose which sample to 'keep' in the histogram at random. You may still use all of the clustered sampling for geostatistical analysis, of course. The semi-variogram and kriging techniques are not affected by clustering. In fact, one of the main reasons for inventing kriging was to make full use of every one of clustered and/or preferentially sited sampling. The term 'declustering' became popular around 1982/83 and is first used widely in the proceedings of the geostatistical congress held at Lake Tahoe in September 1983. Isobel Clark http://uk.geocities.com/drisobelclark __ Do You Yahoo!? Everything you'll ever need on one web page from News and Sport to Email and Music Charts http://uk.my.yahoo.com -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
RE: AI-GEOSTATS: Declustering
I am slightly confused: ... if sampling is clustered preferentially in e.g. higher values areas, would this not bias the semi-variogram for the first few lags?...at least if, as it can happen, the variance is related to the mean. The semi-variogram is calculated on the difference between the two sample values. If the basic assumptions for semi-variogram construction are correct, differences are unrelated to the actual value of each sample or to the actual absolute location of the pair. Therefore, clustering does not influence the semi-variogram. If you have a situation where variance is related to the mean, e.g. with highly skewed data, you need to transform these values in some way before constructing a semi-variogram. This is true whether or not you have clustered sampling. Absolutely regular sampling will not give you a valid semi-variogram if you violate the assumptions upon which it is based. What about the effects of the possible over-estimation of the global mean due to clustering? If you are estimating the global mean based on a distribution model, you need to decluster. If you are estimating the global meaning on the basis of a kriged grid, you do not need to decluster as the kriging system does that for you. You can experiment with these questions using our totally free unlimited kriging game. This can be found in my 'briefcase' at http://uk.geocities.com/drisobelclark/briefcase.html Does this help? Isobel Clark __ Do You Yahoo!? Everything you'll ever need on one web page from News and Sport to Email and Music Charts http://uk.my.yahoo.com -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
AI-GEOSTATS: Re: Kriging of multiple samples
If you have multipl esamples at certain locations, what you can do is to modify the diagonal entry in your kriging system. Instead of gamma(0)=0 put in gamma(0)=(n-1)/n times nugget effect. This tells the kriging system you have replicates and it will adjust weights and optimal estimator accordingly. This is documented in Matheron's original works. Isobel Clark http://uk.geocities.com/drisobelclark Do You Yahoo!? Get your free @yahoo.co.uk address at http://mail.yahoo.co.uk or your free @yahoo.ie address at http://mail.yahoo.ie -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
AI-GEOSTATS: viruses
Warning If you get an empty e-mail with a return address which starts with the underscore, delete it off your system as quickly as you can. Nokia 5510 looks weird sounds great. Go to http://uk.promotions.yahoo.com/nokia/ discover and win it! The competition ends 16 th of December 2001. -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: Extreme values?
My question is: How to deal with the extreme/outlying values in a data set? The real priority is to establish why you have extreme highs. For example: (1) is there a high imprecision in measuring the values, so that the sample observations are actually inaccurate? If so, is it relative to the value or a flat error? (2) do you have a skewed distribution of values? (3) do you have two (or more) populations, only one of which gives the high values? and there may be others. Once you determine the reason for extreme values, then you can more objectively know how to deal with them. For example, if you think (2) is most likely than look at transformations or distribution-free approaches to geostatistics. You can find some of my papers in dealing with positivel skewed distributions at: http://uk.geocities.com/drisobelclark/resume/Publications.html If (3) is more likely - as may be probable is your are looking at an area where samples may be 'background' or 'contaminated' - you really need to identify the populations first. Then you may be able to apply a mixture model together with indicator geostatistical approaches. If (1) is your problem, then you may be able to use a rough non-parametric approach to get to cross validation. The 'error statistics' in a cross validation exercise will often assist in identifying erroneous sample measurements. Hope this helps Isobel Clark __ Do You Yahoo!? Everything you'll ever need on one web page from News and Sport to Email and Music Charts http://uk.my.yahoo.com -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: Search Strategy
Julhendra That is what your semi-variogram is for. Determine maximum distance and anisotropy (change with direction) from your experimental semi-variograms. Your search strategy should also change with the shape of your blast layout. Single blast patterns are usually 'long and thin', meaning that a circular search would be less than optimal. I don't know of any papers which discuss this, but you can see our strategy in the kriging game. This is freely downloadable at: http://uk.geocities.com/drisobelclark/briefcase.html and allows you to experiment with search patterns and changes in semi-variogram model. It also allows you to see the difference between kriging as a 'point' estimation method (for mapping) and kriging an average over a blast area. Unfortunately, this free package is only 2d, but you may find it useful. One other point you may find useful. In my experience, working in 3d reduces to using the previous bench blastholes. A full 3d approach is only useful if you have good diamond or percussion drilling within the search volume. If you are going to combine sampling types, you need to determine whether the samples are compatible or to use a co-kriging approach. Isobel Clark --- Julhendra Solin [EMAIL PROTECTED] wrote: Dear All, I am working on blasthole interpolation in open pit mine. Interpolation using ordinary kriging and grades interpolated also from above bench. Blasthole spacing about 10 m and bench height 15 m. Anybody could help me how to determine search distance and min/max of number of samples to krige the grade. May be some technical paper related to it. Thanks. Jul -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org __ Do You Yahoo!? Everything you'll ever need on one web page from News and Sport to Email and Music Charts http://uk.my.yahoo.com -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: Dealing with Universal Kriging
Rubens Your approach has been long used in hydrology and similar fields with much success. The problem with the standard deviation is that it does not include the the 'error' on the estimation of the true drift. To get a composite error you would either have to (a) add your kriging variance to some sort of classical regression variance to get a composite one; (b) use a Universal Kriging (or generalised covariance) approach to estimate the surface with the drift included. In our experience, your estimated surface will not change but your kriging variances will increase slightly. Isobel Clark __ Do You Yahoo!? Everything you'll ever need on one web page from News and Sport to Email and Music Charts http://uk.my.yahoo.com -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
RE: AI-GEOSTATS: Dealing with Universal Kriging
Alessandro Thanks for the contribution. If Universal Kriging is applied, there is no need for simulation or multi-indicator approaches to get a standard error, it comes with the solution. Isobel __ Do You Yahoo!? Everything you'll ever need on one web page from News and Sport to Email and Music Charts http://uk.my.yahoo.com -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: variogram at zero ( gamma(0) ) in the kriging
Jack There is a schism in the geostatistical community between those who do and those who don't make gamma(0) equal to 0. Some people argue that the nugget effect is 'sampling error' and that gamma(0) should equal c0 so that kriging does not honour the data values. It also makes your kriging variances smaller (emphasis). I (personally) find it a bit weird to have smaller supposed errors if you do not trust your data. Software packages differ as to whether they do or do not go to zero. Simplest way to check is to replace your nugget effect by a spherical component with a very short range of influence and see if your answers change. Isobel Clark http://geoecosse.bizland.com/pg2000.htm __ Do You Yahoo!? Everything you'll ever need on one web page from News and Sport to Email and Music Charts http://uk.my.yahoo.com -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
AI-GEOSTATS: Risk Assessment with Gaussian Simulation?
My tuppence worth. The major advantages of simulation as a risk assessment tool lie in the cases where you are trying to derive some conclusion from the data rather than just look at the values themselves. For example, see Bill and my papers at Battelle Conference 1987 or the paper at the Geostat Avignon in 1988. There are oters. All of these are available in Word format for download at my page http://uk.geocities.com/drisobelclark/resume/Publications.html We were trying to derive the travel path of a particle given the pressure of fluid in an aquifer. Not a linear transform by anyone's standards. Isobel Clark __ Do You Yahoo!? Everything you'll ever need on one web page from News and Sport to Email and Music Charts http://uk.my.yahoo.com -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: Log transformation and zeros
Ernesto
There are several ways of tackling skewed data with
zeroes and I am sure you will get emails from
proponents of this or that other contributor.
Ways which I have found useful:
(1) try a lognormal probability plot and see whether
you have a straight line or if it drops off the line
at low values. This is indicative of a three parameter
lognormal distribution which needs an additive
constant. Find the additive constant that makes the
line straightest (my criterion) or the skewness
closest to zero (Sichel's recommendation). You can
find this described in my 1987 paper following
Sichel's definitive works. Full copy at
http://uk.geocities.com/drisobelclark/resume/Publications.html
{paper titled turning the tables
(2) treat the zeroes as a different population. Are
they zero because there are no fish there or because
you didn't catch any? If the later, use an indicator
approach to separate the 'no fish' population from the
'some fish' one. Then do your lognormal stuff on the
'some fish' and recombine for final results.
(3) - not so nice: use the probability plot as
suggested above to choose a 'threshhold' value to
replace the zeroes. This assumes that all areas
sampled are 'some fish' areas and you just didn't
catch any.
Isobel Clark
http://uk.geocities.com/geoecosse/news.html
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Re: AI-GEOSTATS: anisotropic nugget
There is software around which will allow you to define different nugget effects in different directions, but I would not put any bets on the outcome! It looks like you have a short range component which cannot be seen because of the spacing of your data. Try adding a spherical component with a shorter range and a component sill of the right size to make the nugget effect equal in all directions. I would. Isobel Clark http://geoecosse.bizland.com __ Do You Yahoo!? Everything you'll ever need on one web page from News and Sport to Email and Music Charts http://uk.my.yahoo.com -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: gaussian model
Carolina The gaussian semi-variogram model is so-called because the formula is basically identical to that for the Normal (or gaussian) probability distribution. There is no other necessary link with the Normal distribution. Isobel (Clark) http://uk.geocities.com/geoecosse/news.html __ Do You Yahoo!? Everything you'll ever need on one web page from News and Sport to Email and Music Charts http://uk.my.yahoo.com -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: curve fitting summary
To be a valid covariance function, it must be positive definite (as a function). In particular this implies that the function is bounded (hence no polynomials) I hate to sound ignorant here, but aren't most of the standard semi-variogram models polynomials of one kind or another? I remember seeing a paper a few years ago by a coupl eof blokes from Pretoria University on a generalised polynomial fit which would be positive definite. I don't have it to hand but can probably track it down if given sufficient motivation ;-) Isobel Clark http://geoecosse.bizland.com/news.html __ Do You Yahoo!? Everything you'll ever need on one web page from News and Sport to Email and Music Charts http://uk.my.yahoo.com -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: Standard deviation, Variance
The reason is simple and comprehensive Assume a population with ANY distribution of elements. Then randomly select a number of sample elements from the population to characterize the underlying population. That distribution of sample elements ALWAYS tends toward a normal [Gaussian] distribution. And the mean and standard deviation of the sample distribution are unbiased representations of the mean and standard deviation of the underlying population. Things have obviously changed since I was a lad. I was taught that the Central Limit Theorem was a theorem NOT a law. There are distributions which do not conform to this behaviour and (alas for us) the lognormal is one of them. The Central Limit theorem also does not apply to mixed distributions or in cases of non-stationarity. Mind you, neither does geostatistics Isobel Clark http://geoecosse.bizland.com/news.html __ Do You Yahoo!? Everything you'll ever need on one web page from News and Sport to Email and Music Charts http://uk.my.yahoo.com -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Fwd: Re: AI-GEOSTATS: Standard deviation, Variance
Thank you Isobel --- Donald E. Myers [EMAIL PROTECTED] wrote: Date: Fri, 06 Dec 2002 12:05:54 -0700 From: Donald E. Myers [EMAIL PROTECTED] To: Isobel Clark [EMAIL PROTECTED] Subject: Re: AI-GEOSTATS: Standard deviation, Variance I stand corrected on mistakingly attributing the description of the CLT to you Donald Myers Isobel Clark wrote: Thanks to Rubén and Digby for pointing out what I had misunderstood about Don Myers' email. It had not occurred to me (duh) that the lines starting '' would be read as being from me rather than part of a forwarded email. Another score on the dumb side. Apologies for the strong reaction to Don's email if (on this occasion) he was not criticising my contribution. Isobel http://uk.geocities.com/drisobelclark __ Do You Yahoo!? Everything you'll ever need on one web page from News and Sport to Email and Music Charts http://uk.my.yahoo.com -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org __ Do You Yahoo!? Everything you'll ever need on one web page from News and Sport to Email and Music Charts http://uk.my.yahoo.com -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: Calculating averages
Hi Craig The average of a product will only equal the product of the averages if the two numbers are completely independent of one another. This is exactly analogous to the calculation of a covariance in statistics. Isobel http://uk.geocities.com/drisobelclark __ Do You Yahoo!? Everything you'll ever need on one web page from News and Sport to Email and Music Charts http://uk.my.yahoo.com -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: KRIGING EVALUATION
Fabrizio If you want to limit your estimates by kriging variance, the obvious place to stop would be where the kriging variance becomes equal to the total sill on your semi-variogram (if you have one) or to the estimated population variance for your sample values. A kriging variance above this value, basically, says that your estimate is a worse estimator than just using the population mean. Isobel Clark http://geoecosse.bizland.com/news.html __ Do You Yahoo!? Everything you'll ever need on one web page from News and Sport to Email and Music Charts http://uk.my.yahoo.com -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: Kriging Error vs variance
Russell Absolutely on the spot. We call this the 'ygiagam' criterion (your guess is as good as mine) ;-) Isobel Clark http://geoecosse.bizland.com/news.html __ Do You Yahoo!? Everything you'll ever need on one web page from News and Sport to Email and Music Charts http://uk.my.yahoo.com -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: Observations with a known standard deviation
Soeren I presume what you have is a sort of 'analytical error' for each sample? That is, the standard deviation for two samples at the same location around the 'true value' at the same location? In this case, you can put the variance down the diagonal of your kriging system to obtain optimal weights under the uncertainty admitted for your data values. You would need to be careful that the 'analytical variance' was not greater than the nugget effect of the semi-variogram model. The kriging system would be similar to that obtained when the sample is not treated as a 'point', but rather as a volume. This results in a lower kriging variance than using zero on the diagonal, so to compensate you should probably add the complete 'analytical variance' back on to get realistic estimation variances. There seems to be a lot of confusion in the books (and software) about what happens if you have a significant replication variance. Isobel Clark http://geoecosse.bizland.com/news.html __ Do You Yahoo!? Everything you'll ever need on one web page from News and Sport to Email and Music Charts http://uk.my.yahoo.com -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: Question about Block Lognormal Kriging.
Adrian I don't do simple kriging, but both forms of the complete backtransform are available in the papers presented at Geocongress 1998 and Pribram 1999. These are available at http://uk.geocities.com/drisobelclark/resume/Publications.html If you have any problems downloading, let me know. Isobel Clark http://geoecosse.bizland.com/news.html --- Adrian_Martínez_Vargas [EMAIL PROTECTED] wrote: Question about Block Lognormal Kriging. For the Point Lognormal Kriging the unbiased estimator of z* is z*(u)=exp[y*(u) + SigmaSK^2(u)/2] where: SigmaSK^2 simple lognormal kriging variante how to get and unbiased estimator for: a) Simple Block Lognormal Kriging. b) Ordinary Block Lognormal Kriging. c) Ordinary Point Lognormal Kriging. __ Do You Yahoo!? Everything you'll ever need on one web page from News and Sport to Email and Music Charts http://uk.my.yahoo.com -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: Estimation of the cross semivariogram
Soeren What you have here is sometimes known as a co-located cross semi-variogram and only pairs of samples with both variables can be included in its calculation. There is a non-co-located semi-variogram (see Cressie's book for example) which looks like gamma(h)=1/2N(h)*sum((z_i-y_j^2) This works best if the variables are standardised (same mean, same standard deviation) and uses all of the samples with either variable. Isobel Clark http://geoecosse.bizland.com/news.html --- Soeren Nymand Lophaven [EMAIL PROTECTED] wrote: Dear list I have a question regarding estimation of the cross semivariogram, given by: gamma(h)=1/2N(h)*sum((z_i-z_j)(y_i-y_j)) where y and z are the two variables. My question simply is: Do y and z have to be measured at the same locations in order to estimate the cross semivariogram ?? Best regards / Venlig hilsen Søren Lophaven ** Master of Science in Engineering| Ph.D. student Informatics and Mathematical Modelling | Building 321, Room 011 Technical University of Denmark | 2800 kgs. Lyngby, Denmark E-mail: [EMAIL PROTECTED] | http://www.imm.dtu.dk/~snl Telephone: +45 45253419 | ** -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org __ Do You Yahoo!? Everything you'll ever need on one web page from News and Sport to Email and Music Charts http://uk.my.yahoo.com -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: Variograms models
Matheron used the term spherical to describe the semi-variogram model which represents the concept of two overlapping 'spheres of influence'. The formula is actually the geometric calculation of the amount by which two spheres of diameter 'a' (range of influence) do NOT overlap when their centres are separated by a given distance. The exponential model contains an exponential term and is exactly equivalent to the 'exponential decay' beloved of economists and other predicters. BTW: the Gaussian is so-called simply because it is the same shape as a Normal cumulative frequency plot (ogive). Isobel Clark http://uk.geocities.com/drisobelclark/resume/Publications.html --- Serele, Charles [EMAIL PROTECTED] wrote: Hi all, Does anyboby can explain to me the origin of the variogram models: spherical and exponential ? Why the names spherical and exponential ? Sincerely Charles __ Do You Yahoo!? Everything you'll ever need on one web page from News and Sport to Email and Music Charts http://uk.my.yahoo.com -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: Cross variogram
Digby That is the 'traditional' cross semi-variogram as discussed in Matheron's original work. Now also known as a co-located cross semi-variogram. There is a non-co-located cross semi-variogram which goes something like: gamma(h)=1/2N(h) SUMi,j(vi-uj)^2 which is always positive. However, you probably have to standardise u and v to get meaningful results (which you can't really do with skewed data). Noel Cressie has shown in a paper in Math Geol that a semi-variogram calculated on logarithms is the same generically as a general relative semi-variogram. I should think that conclusion probably holds for cross semi-variograms too. Calculating on logarithms is computationally simpler than calculating a relative semi-variogram. Isobel Clark http://uk.geocities.com/drisobelclark --- Digby Millikan [EMAIL PROTECTED] wrote: Hello everyone, The forumlea which I have obtained for the cross variogram is; gamma(h)=1/2N(h) SUMi,j(vi-vj)(ui-uj) Is it correct then that the product of the differences can be negative in cases. Digby __ Do You Yahoo!? Everything you'll ever need on one web page from News and Sport to Email and Music Charts http://uk.my.yahoo.com -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: large error correlation coefficient?
I have performed a jacknife estimation of e variable V1* in a 3D space, the reference file have the true values of V1. Then I get the local error as ERR=V1-V1*. The problem is that correlation coefficient have large values for V1 and the other variables (0.7-0.9) and by theory the error must to be independent of the V1. Sorry, that's not true. The error is independent of V1* but never of V1, especially if you are using a linear estimator such as kriging. Why it happen, it is really dangerous in resource estimation? This is known as conditional bias and, in short, YES! This effect has been documented for 50 years and has variously been known as the regression effect, the mine call factor, the volume/variance effect, conditional bias and many other things (not all of them polite!). Isobel Clark http://geoecosse.bizland.com/whatsnew.htm Want to chat instantly with your online friends? Get the FREE Yahoo! Messenger http://uk.messenger.yahoo.com/ -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: bounds of IK variograms
Jörg Don't confuse indicator variables with classical correlation coefficients. The maximum possible on your semi-variogram will be where all differences are 1. That is every pair is (1-0). And, of course, divided by 2. So the absolute maximum an indicator semi-variogram can show is 0.5. Computationally then, if 90% of your data are 1s and 10% are zeroes, the semi-variogram can still (theoretically) reach 0.5 if the 90% are all clustered and the 10% are, say, peripheral. Isobel http://uk.geocities.com/drisobelclark Want to chat instantly with your online friends? Get the FREE Yahoo! Messenger http://uk.messenger.yahoo.com/ -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: global vs local ordinary kriging
Ulrich Depends how powerful your computer is, what algorithm you use to solve equations and how many data you have. Isobel http://geoecosse.bizland.com/0toKriging.htm Want to chat instantly with your online friends? Get the FREE Yahoo! Messenger http://uk.messenger.yahoo.com/ -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: [AI-GEOSTATS: global vs local ordinary kriging]
Maybe it is worth pointing out that Ordinary Kriging with a 'global neighbourhood' (using all the points in simple speak) is the same as Simple Kriging with a neighbourhood which extends to the range of influence of the semi-variogram model (if any). Given this fact, you would be computationally safer to do Simple Kriging - otherwise known as kriging with known mean and saving yourself the problems of enormous and sparse matrix solutions. The only overhead to Simple Kriging is producing a reliable estimate of the global mean and, to be realistic, a standard error associated with it. Isobel Clark http://geoecosse.bizland.com/courses.htm Want to chat instantly with your online friends? Get the FREE Yahoo! Messenger http://uk.messenger.yahoo.com/ -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: Log-normal back transform in Webster Oliver
Gregoire Thank you for pointing out the lognormal section in Webster Oliver. I must confess I hadn't got round to looking at it in detail. Their simplification of the lognormal variance is based on the assumptions (see p.179) that: (a) the lagrangian multiplier would be close to zero if the mean is well known (b) the simple kriging weights would sum close to one if the data is dense enough The assumption (a) is one which has also been asserted by Peter Dowd in some of his publications. From practical experience (over 30 years) we find that the lagrangian multiplier is seldom close to zero and, in fact, where data is dense will tend to be large and negative. We have also done some fairly intensive practical studies of simple kriging and found that, where data is dense, the kriging weights will tend to be very much greater than 1 so that the wieght applied to the known mean will be large and negative. Where data is sparse, weights sum to very much less than 1 so that poorly sampled areas are allocated the 'global' mean. Equations 8.35 and 8.39 rely on these assumptions and the implicit one that the only difference between the variance of the real values and that of the estimates is due to the simple kriging variance (i.e. no condiitonal bias). It has been asserted by several authors that simple kriging corrects for conditional bias. Would that that was true!! Equation 8.36 for ordinary kriging is correct, but we prefer to use Sichel's proper lognormal confidence intervals rather than back-transform the variance as shown in equation 8.37. To use this form you would have to assume that your errors were Normal even though your data was lognormal. I think there is a typo in equation 8.38 and the subscript 'Y' should be 'SK' to bring it into line with the other formulae. The definitive math on the lognormal backtransform can be found in Noel Cressie's book in equation 3.2.40 (for both types of kriging). Simpler explanations of the same form can be found in some of my papers at http://uk.geocities.com/drisobelclark/resume/Publications.html (note the capital P and look for papers in the second half of the 1990s). Isobel Clark http://geoecosse.bizland.com/whatsnew.htm Want to chat instantly with your online friends? Get the FREE Yahoo! Messenger http://uk.messenger.yahoo.com/ -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: stratified kriging
Oliver We have had some success with 'modelling' stuff like soil types using indicator variables. This gives you a 'probability' map as to whether or not you are in a particular soil type (or whatever) which you could then use to modify the inclusion (or perhaps the weighting?) of your samples when kriging. Isobel http://ecosse.ontheweb.com Want to chat instantly with your online friends? Get the FREE Yahoo! Messenger http://uk.messenger.yahoo.com/ -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: Simulation and trends
Chris
Could I be incredibly obvious and suggest that, if you
use Universal Kriging, the trend is fitted and
simulated automatically with SGS. This is one of the
major advantages of SGS over approaches like Turning
Bands or Monte-Carlo -- if you can krige it, you can
simulate it.
There is a lot of evidence in the literature, dating
back to the early '80s that kriging residuals and
adding back the trend gives you pretty much the same
estimated surface as Universal Kriging. However, what
it doesn't do is give you the right standard error
since it doesn't allow for the trend fitting error. So
I would hazard a guess that simulations done this way
would underestimate the 'true' variability.
Isobel {Clark}
http://drisobelclark.ontheweb.com
PS: could I take this opportunity to remind anyone
interested that the IAMG 2003 is rapidly approaching.
If you haven't registered yet, sort yourself out at
http://www.iamg2003.com or follow the links from our
page at http://ecosse.ontheweb.com/whatsnew.htm
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Re: AI-GEOSTATS: Simulation and trends
Adrian Thank you for the reminder of one of the strengths of Turning Bands. Certainly I have no argument with your points. However Chris' question was about how to include trend in SGS and that is what my answer is about. Isobel http://ecosse.ontheweb.com Want to chat instantly with your online friends? Get the FREE Yahoo! Messenger http://uk.messenger.yahoo.com/ -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: values normalisation with a lot of zero!
I can't make a transformation by log(x+1) because the result should be the same!! I don't understand your point here about the additive constant. You also have to be careful with regressions on log transforms because the 'back transform' is not simply take the anti-log and subtract the added constant. Isobel Clark http://ecosse.ontheweb.com/whatsnew.htm Want to chat instantly with your online friends? Get the FREE Yahoo! Messenger http://uk.messenger.yahoo.com/ -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
AI-GEOSTATS: Jackknife Literature Source
Peter May I suggest Noel Cressie's book Statistics for Spatial Data (Wiley). He has extensive discussion of jack knives, bootstraps and such like and an extensive bibliography. Isobel Clark http://geoecosse.bizland.com/whatsnew.htm Want to chat instantly with your online friends? Get the FREE Yahoo! Messenger http://uk.messenger.yahoo.com/ -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: Lag - Distance, Variogram / Semivariogram
Ursula 5.5 x 20 metres Choosing a 5 metres lag, the variance values are too high in the first 3 -4 lags. This is possibly because you have some competition effect between orchids. For a square grid, we usually recommend an interval 20% of the grid spacing, so you don't get diagonals lumped in with 'straight' directions. This would suggest that you should try a 1 metre lag, which is probably overkill. The other alternative is to construct directional semi-variograms and specify the correct lag for each direction, to see what differences you get. My second question is what is the difference between a variogram and a semivariogram ? As a general rule a variogram is a semi-variogram constructed by someone lax in their terminology. No software I know calculates the true variogram (twice the semi-variogram). The correlogram is simply the semi-variogram upside down and standardised to vary between -1 and +1. The disadvantage of this approach (or the covariance function is that it is difficult to assess the nugget effect accurately. You should be concerned about your variance as it provides essential information about teh variability of your phenomenon. Isobel Clark http://ecosse.ontheweb.com/whatsnew.htm Want to chat instantly with your online friends? Get the FREE Yahoo! Messenger http://mail.messenger.yahoo.co.uk -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: bad regression between predicted and measured
Duccio There are many reasons why your interpolations may not be working. A few of these are: # you are beyond the range of influence of any distance relationship, that is you have too widely spaced sampling. # your data may have a skewed or other non-Gaussian distribution which makes both semi-variogram and correlation calculations invalid # you may have discontinuities, trends or anisotropies which have not been factored into your model Isobel http://drisobelclark.ontheweb.com Want to chat instantly with your online friends? Get the FREE Yahoo! Messenger http://mail.messenger.yahoo.co.uk -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: Kt estimation variance
Sebastiano Large kriging variances have nothing to do with negative weights. The two are completely different phenomena - especially in Universal Kriging. In Ordinary Kriging the estimation variance can become as high as two times the total sill of the semi-variogram. This is a theoretical fact(?) and you can derive the answer by simply trying to estimate the value at one point from a single sample at or beyond the range of influence from this location. That is, a weight of +1!! In Universal Kriging, the weights often become negative because the system is trying to force the estimated point to lie on the trend of the samples. Sometimes it can only do this by using negative weights. There is no problem here, unless you have extremely high 'erratic' residuals. In this case, you should probably resolve that problem before trying kriging. If the variance becomes very high in Universal Kriging it is probably because you are extrapolating into sparsely sampled areas. Remember you are trying to estimate the trend as well as the 'residual' value and this contributes to higher variances. You should widen your search radius to include more samples than with Ordinary Kriging. You can see how all this works with our free kriging game. If your data is in Geo-EAS form or a simple CSV file, you can read it into Krigame and see the equations and the solutions. Then vary search parameters etc to see how they are affected. You might want to download our Tutorial 3 which discusses Universal Kriging with the Wolfcamp data. All available at http://geoecosse.bizland.com/softwares with no restriction on use or distribution. Isobel Want to chat instantly with your online friends? Get the FREE Yahoo! Messenger http://mail.messenger.yahoo.co.uk -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
AI-GEOSTATS: Nugget to Sill Ratio
Jul The nugget effect is the (semi) variance between two samples which might be taken at almost exactly the same spot. Or, expressed otherwise, the variance of replicated samples. The total sill is the variance of values within your data set (or, more strictly, within all possible samples). Thus the nugget to not-nugget ratio is the proportion of the variation you can expect to predict with a spatial model, whilst the nugget part is that variation you cannot predict no matter how closely you sample. Isobel http://geoecosse.bizland.com/books.htm Want to chat instantly with your online friends? Get the FREE Yahoo! Messenger http://mail.messenger.yahoo.co.uk -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
AI-GEOSTATS: Re: co-kriging on data with spatial trends
Sigrun Calculating of cross semi-variograms has to be done on residuals if there is a trend, just like any single variable semi-variogram. You might find our MUCK papers useful, as we were co-kriging two variables both with trend back when we first started in the 1980s. You can find our papers at http://uk.geocities.com/drisobelclark/resume/Publications.html (note the capital P). Your other question about search radii. When trend is present, you need to enlarge your search radius past the range of influence to get enough samples to condition the equations properly - that is, to solve for the trend as well as the weights. You can see how this works with uor kriging game, free to all at http://geoecosse.bizland.com/softwares Hope this helps Isobel [Clark] Download Yahoo! Messenger now for a chance to win Live At Knebworth DVDs http://www.yahoo.co.uk/robbiewilliams -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: Moran scatterplot
Monica The simplest solution to your problem is to use probability paper. If you do not have easy access to this, you can download a free graph paper plotter from http://perso.easynet.fr/~philimar There are also simple algorithms to produce your own. Two populations show up on a probability plot as a line with a definite 'kink' in it. Skewed distributions should be plotted on a logarithmic scale. Explanations can be found in my paper ROKE paper (CG 1977) which is computer oriented or in my IMGC paper (1993). Both downloadable from http://uk.geocities.com/drisobelclark/resume/Publications.html Isobel Download Yahoo! Messenger now for a chance to win Live At Knebworth DVDs http://www.yahoo.co.uk/robbiewilliams -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: log-normal kriging error
Marta I am not familiar with the software you are using, but it looks like your lognormal standard errors are being back-transformed into 'raw' units. If this is the case part of the backtransform is to multiply the 'relative standard error' by the actual value of the estimate. That is, if your estimate is 0.52, the backtransformed standard error is multiplied by 0.52. If the estimate is 520, it is multiplied by 520. If you do a ratio between the standard error and the estimate, you will probably get equivalent 'relative' errors. We find it better to leave the standard errors in logarithms and use Sichel type confidence interval, using the lognormal model. Isobel http://uk.geocities.com/drisobelclark Download Yahoo! Messenger now for a chance to win Live At Knebworth DVDs http://www.yahoo.co.uk/robbiewilliams -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
AI-GEOSTATS: Re: sparse data problem
Everybody (especially Gali!) Just to put the base case in perspective. Many half-billion dollar projects in Southern Africa have been evaluated and floated on the stock exchange on the basis of 5 or 6 holes. When a sample costs a couple of million dollars to acquire, there is little point in hoping for more. We use an extremely well sampled case in our (free) tutorial analyses. Look for the GASA data which has 27 samples. An embarrassement of riches in the mid-1980s, I can assure you. Isobel Clark http://geoecosse.bizland.com/softwares Download Yahoo! Messenger now for a chance to win Live At Knebworth DVDs http://www.yahoo.co.uk/robbiewilliams -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
AI-GEOSTATS: basic theoretical question
Hi Koen Firstly, I have to tell you that many people would kill for the type of data you have - it is absolutely ideal for trying out a geostatistical approach. Secondly, can I suggest that you work through our free tutorials - especially Tutorials 2 and 3 - which can be downloaded from http://geoecosse.bizland.com/softwares in Word format. If you need pdf or some other format, please let us know. These Tutorials take you from first look at data through to kriging in a fairly straightforward manner with a tutorial data set (which is also downloadable). Please let me know if you have any problems with this, or further questions. Isobel [Clark] http://geoecosse.bizland.com/whatsnew.htm BT Yahoo! Broadband - Save £80 when you order online today. Hurry! Offer ends 21st December 2003. The way the internet was meant to be. http://uk.rd.yahoo.com/evt=21064/*http://btyahoo.yahoo.co.uk -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: maximum kriging variance with standardized sill
is it right to assume the maximum kriging variance to be =2 when using a variogram with a standardized sill of 1 ?? Yes, if you are estimating the value at a point from only one sample which is outside its range of influence. Isobel http://uk.geocities.com/drisobelclark/practica.htm BT Yahoo! Broadband - Save £80 when you order online today. Hurry! Offer ends 21st December 2003. The way the internet was meant to be. http://uk.rd.yahoo.com/evt=21064/*http://btyahoo.yahoo.co.uk -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: Hypothesis Testing in a Spatial Framework
Warren We have had some success with a sort of hypothesis test in this regard. I had a task some years back to prove that the first area mined in a deposit was not significantly lower than could be expected by chance selection. We used a combination between 'between block variance' and a sort of cutoff analysis. It helps if your samples have a simple distribution like Normal or lognormal. Basically, you work out the probability that a block of a certain size would have a value that low (in our case). It is, effectively, a simple application of volume/variance. Chapter 3 in my 'old' book which can be read (or downloaded) at http://uk.geocities.com/practica.htm Isobel Yahoo! Messenger - Communicate instantly...Ping your friends today! Download Messenger Now http://uk.messenger.yahoo.com/download/index.html -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
AI-GEOSTATS: Re: Rules
Dear Gregoire (and everyone else) I did not consider my contribution to be an advert but a public information notice. Readers such as Michele Scardi who see this as cheap advertising, attribute me with far more subtlety than I actually possess. The tolerance of our readers seems to stretch to endless user support for GSTAT/R etc and for other people promoting conferences and courses - most recent example being Gina Clemmer [EMAIL PROTECTED] who placed a formal advertisement for Mapping Los Angeles: An Introduction to GIS on 28th January 2004 without a single indignant comment from any member of the list. Isobel Clark http://geoecosse.bizland.com/whatsnew.htm ___ BT Yahoo! Broadband - Free modem offer, sign up online today and save £80 http://btyahoo.yahoo.co.uk -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: Re: polygon kriging
Chaosheng This is very true that if you grid a grid of points inside a polygonal area then average them, you get exactly the same answer as if you kriged the polygon average directly. The differences are two: (1) you have to do at least 64 krigings to get within 1% of the correct average answer (see my paper at the first Geostat Congress in 1975) (2) if you do one kriging for the polygon average, you get the kriging variance for the polygon average. You can derive this from the discretised point kriging variances but you have to do even more work (64 squared) than in (1). Isobel http://geoecosse.bizland.com/whatsnew.htm ___ Yahoo! Messenger - Communicate instantly...Ping your friends today! Download Messenger Now http://uk.messenger.yahoo.com/download/index.html -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
Re: AI-GEOSTATS: modelling_dem_point
Ines It isn't usually a good idea to go pushing your data to where you would like them to be. A good way to determine natural spacing is to carry out a 'nearest neighbour' analysis. If data are on a grid, the best spacing is 0.2 times grid size. This keeps single grid spacing separate from single diagonal spacing and so on. Isobel http://geoecosse.bizland.com/whatsnew.htm ___ Yahoo! Messenger - Communicate instantly...Ping your friends today! Download Messenger Now http://uk.messenger.yahoo.com/download/index.html -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
AI-GEOSTATS: Re: average semi-variogram
Koen I think it's called a block to block variogram average, not sure. It is called the within block variance. Block to block variance is the variance between block averages - i.e. from block to block. As I explained, I'm looking for an easy way to estimate the gamma(V,V) value. If you have a standard semi-variogram model such as the spherical or exponential, the mathematical formulae for two dimensional blocks are published in various issues of Computers and Geosciences. Point approximations are only necessary if you have a non-readitional model or rotational geometric anisotropy. I used matlab to code for the distances between pairs but, it takes so much time compared to . Most software packages use the symmetry of the block so that only about one-quarter of the calculation need to be carried out. You can get the within block variance from our kriging game for all the models we cover. It is written onto the screen and the ghost file as you work. Just select the option to estimate a rectangular block. http://geoecosse.bizland.com/softwares Isobel ___ Yahoo! Messenger - Communicate instantly...Ping your friends today! Download Messenger Now http://uk.messenger.yahoo.com/download/index.html -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
AI-GEOSTATS: Re: mixtures of populations
Hello All The common 'Normal Score' transform assumes one population. Transformations such as rank or logarithm do not assume one population. The best way to identify likely mixtures is with programs such as Peter MacDonald's Mix (cited in Ruben's email I think): http://www.math.mcmaster.ca/peter/mix/mix31.html or with probability plots. Many software packages have these and mixtures are easily identifiable by break-points or points of inflexion in the plot. For those (like myself) without easy access to libraries, there are a couple of papers which describe (geological) applications and using a combination of indicator and ordinary kriging to solve some problems. Papers can be found at http://uk.geocities.com/drisobelclark/resume follow the publications link. Look for my 1974 paper, now available in pdf format, the 1993 IMGC paper and the 1992 Troia paper with Jonathan Vieler. We have had good experience with this approach for 30 years in fields as diverse as mineral resource estimation and seabird preservation. Isobel Clark http://geoecosse.bizland.com/courses.htm ___ Yahoo! Messenger - Communicate instantly...Ping your friends today! Download Messenger Now http://uk.messenger.yahoo.com/download/index.html -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and unsubscribe ai-geostats followed by end on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
AI-GEOSTATS: Re: mixtures of populations
AH me, the English language slips away from me again.
I said that the PRESENCE {pardon the capitals, no way
to italicise email} of more than one population is
indicated by the points of inflexion on the
probability plot. Not that these were breakpoints
between populations.
Normal (or lognormal) populations overlap. The break
point in the probability plot allows us to distinguish
between data which are skewed and multiple
populations. Skewed data give curved probability
plots. Mixtures of populations give plots with abrupt
changes in slope. These are very rarely equivalent to
'equal probability' points - that is, statistical
break points between the population. But, they are a
good place to start looking ;-)
Once you have deduced that multiple populations are
present there are lots of things you can do, including
simple stuff like post-plotting an indicator transform
of the data at various threshholds just to see if
there is any spatial pattern obvious to the naked eye.
In many cases, ordinary kriging can proceed even with
a mixture, since it only requires second-order
stationarity not the existance of one single
population.
In 34 years of searching, I have never seen a
probability plot with breakpoint(s) which did not have
a matching multiple population explanation. The number
of times I have argued with a 'customer' about this is
legion. In some cases, we have found more populations
than expected (witness my 1993 IGMC paper).
In environmental studies, as in many geological
situations, one would normally expect a broad
background population of readings with the 'pollution'
showing as a more cohesive, generally higher valued
overlying one. Where both exist in the same locality,
it is often difficult to separate them in the data set
because you need both to characterise that area. This
is the case where you would co-krige an indicator and
two populations to get one estimate.
Peter MacDonald's work is pretty definitive in North
America and his MIX program for separating a histogram
out into components has been around for 30 years, to
my knowledge (I met him in 1976 at a Biometrics
Congress!).
There is a great monograph by Alistair Sinclair called
Application of Probability Plots in Mineral
Exploration which costs around $10 from the
Association of Exploration Geochemists and was first
published about 30 years ago. The task of identifying
mineral targets is very like that of identifying
pollution sources or other types of 'secondary'
populations.
It is much better to identify multiple populations
from other knwledge of the site, but this is not
always possible. If you don't know whether or not you
have a mixture, statistical plots are one way of
checking - and very quick and easy to produce
nowadays. I am open to any other suggestions on how
to identify multiple populations when all you have is
the sample data.
Isobel Clark
http://uk.geocities.com/drisobelclark
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Re: [ai-geostats] problem regarding variogram
snehamoy when you say positively skewed do you mean skewed to the left or to the right. If you calculate the skewness coefficient, postive is skewed to the left with a long tail to the right. If your data is skewed to the right, it is negatively skewed. For negative skewness, we have had success with subtracting limestone values from the maximum chemically possible Ca content. Then using a lognormal approach. That is take 58(?)-Ca and then take logs. If you have a variance of 140, you didn't take logarithms yet. Your variance should be the same whether you do the linear transform or not, only the logarithmic or other non-linear transformation would change the variance. Can you clarify? Isobel http://geoecosse.bizland.com/course_brochure.htm Yahoo! Messenger - Communicate instantly...Ping your friends today! Download Messenger Now http://uk.messenger.yahoo.com/download/index.html
[ai-geostats] Re: kriging proportions
Marc-Olivier The simplest solution - in the sense that most packages could handle it - is to carry out a 'nested' indicator analysis. That is: (i) code one of your particle classes as '1' and all other as '0', produce a map of proportion of this class. (ii) remove this particle class from your data. Code the next class as 1 and all others as 0. produce a map of the proportion of this class, given that it is not in the first class. The 'actual' proportion is then P(ii)*(1-P(i)). (iii) If you have more than three classes, you can keep nesting although you tend to run out of data pretty fast. The last class has whatever proportion is left. Proportions such as this which have to add up to 1 or 100% have been the subject of a lot of study, particularly by people such as Vera Pawlowsky-Glahn under the title 'compositional data'. Isobel http://geoecosse.bizland.com/BYOGeostats.htm ___ALL-NEW Yahoo! Messenger - so many all-new ways to express yourself http://uk.messenger.yahoo.com * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
Re: [ai-geostats] variograms
Salah If your data is irregularly spaced, then you need to experiment with 'lag' intervals to balance between (a) getting enough points to see the shape of the graph and (b) getting enough pairs in each point to have some confidence in it. Remember that each point on your graph is an estimate of a variance. Some books give hard-and-fast rules like you have to have 25 pairs in each point but, personally, I think this is fatuous. The real situation is a bit circular -- if you have a regular phenomenon, you can get the shape with few samples and few points; if you have an erratic phenomenon you need many samples and lots of points. Over the years, I have found the folowing useful: i) look at the 'nearest neighbour' or inter-sample distances to see what the 'natural' spacing in your data is. ii) Use that to guide your first choice for lag interval and experiment around that distance. iii) Use the Cressie goodness of fit statistic to help you judge the fit of your model. iv) Use cross validation to help you judge the fit of the model and the behaviour of the kriging errors. If your data is on a grid, life is a lot easier, just use 1/5th of the grid spacing as your lag interval. The usual rule of thumb on number of lags is not to go more than half the extent of your study area. That is, if your study area is 1km on a side, construct your semi-variogram to a maximum of 500 metres. Hope this helps Isobel http://geoecosse.bizland.com/whatsnew.htm ___ALL-NEW Yahoo! Messenger - so many all-new ways to express yourself http://uk.messenger.yahoo.com * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] Re: Kriging Small Blocks
Jul The warning about kriging small blocks is about small relative to the sampling density. For example, less than about one-third of the grid spacing. The warning is the same as the one about 'point' kriging (mapping) The map is too smooth - or, at least, a lot smoother than the real surface would be. High value areas will be under-estimated and low value areas will be over-estimated. If your objective in kriging is to obtain general maps of an area with an idea of where the highs and lows are, then ordinary kriging is sufficient. The over- and under- estimations cancel out on average. In mining applications, where block kriging originated, most applications require a 'cutoff', where values below a certain value are not included in the 'plan'. In this case, mapping or estimating small blocks will result in an over-estimation of 'payable' ground and an under-estimation in average value. In pollution or environmental applications, the areas at risk will be under-estimated as will the true toxicity or risk factors. There are two major ways round this problem: (1) use a non-linear kriging approach such as disjunctive kriging or the multivariate gaussian. Ed Isaacs and Mohan Srivastava's book is th ebest reference for the latter. Rivoirard's book for DK. (2) simulation. There are lots of simulation methods around, which allow you to 'put back the roughness' and get an idea how bad the problem might be. GSLib is pretty good on this. Isobel http://geoecosse.bizland.com/course_brochure.htm If, as in mining, you wish to apply some sort ___ALL-NEW Yahoo! Messenger - so many all-new ways to express yourself http://uk.messenger.yahoo.com * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] Re: Kriging Small Blocks
Nicolau I was talking about kriging before cutoff is applied. If the cutoff is applied to the block estimates my comments stand. If you aply the cutoff to your data first and then krige, you get the opposite problem, because you will over-estimate every value and under-estimate the tonnage. My point (1) is that, if you wish to avoid conditional bias in your kriging, you could consider using a non-linear kriging method such as those mentioned. I have no experience with either, since I follow a different route in the correction of conditional bias in mineral resource estimation. Isobel http://geoecosse.bizland.com/whatsnew.htm --- [EMAIL PROTECTED] wrote: Isobel, So for mining purposes can't we just krige before applying the cut-off criteria? I mean, for most mining applications one will prefer to have a more realistic geologic block model and will always have the chance to evaluate his/her panels under the appropriate cut-off criteria, but applying that criteria after estimating small blocks, right? Could you please explain your point in solution (1) below? Thanks for indicating the literature. Thanks Nicolau Barros Engineer Mine Planning and Production Control Department Mineração Rio do Norte S.A. [EMAIL PROTECTED] +55 (93) 549 8215 Confidencialidade Esse e-mail e possíveis anexos podem possuir informações confidenciais e de interesse somente do destinatário. Portanto, se você recebeu esta mensagem por engano, favor comunicar imediatamente o remetente e deletá-la logo em seguida. Esteja ciente que o uso indevido do conteúdo das informações em questão é estritamente proibido. Confidentiality This message and any possible attached files may contain confidential information and only for interest of the intended recipient. If you have received this message by mistake, please notify the sender and delete the message immediately. Be aware that the unauthorized use of the above-mentioned information is strictly forbidden. -Mensagem original- De: Isobel Clark [mailto:[EMAIL PROTECTED] Enviada em: segunda-feira, 19 de julho de 2004 05:23 Para: [EMAIL PROTECTED] Cc: [EMAIL PROTECTED] Assunto: [ai-geostats] Re: Kriging Small Blocks Jul The warning about kriging small blocks is about small relative to the sampling density. For example, less than about one-third of the grid spacing. The warning is the same as the one about 'point' kriging (mapping) The map is too smooth - or, at least, a lot smoother than the real surface would be. High value areas will be under-estimated and low value areas will be over-estimated. If your objective in kriging is to obtain general maps of an area with an idea of where the highs and lows are, then ordinary kriging is sufficient. The over- and under- estimations cancel out on average. In mining applications, where block kriging originated, most applications require a 'cutoff', where values below a certain value are not included in the 'plan'. In this case, mapping or estimating small blocks will result in an over-estimation of 'payable' ground and an under-estimation in average value. In pollution or environmental applications, the areas at risk will be under-estimated as will the true toxicity or risk factors. There are two major ways round this problem: (1) use a non-linear kriging approach such as disjunctive kriging or the multivariate gaussian. Ed Isaacs and Mohan Srivastava's book is th ebest reference for the latter. Rivoirard's book for DK. (2) simulation. There are lots of simulation methods around, which allow you to 'put back the roughness' and get an idea how bad the problem might be. GSLib is pretty good on this. Isobel http://geoecosse.bizland.com/course_brochure.htm If, as in mining, you wish to apply some sort ___ALL-NEW Yahoo! Messenger - so many all-new ways to express yourself http://uk.messenger.yahoo.com ___ALL-NEW Yahoo! Messenger - so many all-new ways to express yourself http://uk.messenger.yahoo.com * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] Re: Kriging Small Blocks
Ed I would differ from your explanation on one point. If you are merely declaring a mineral resource, i.e. mineral in the ground, then the conditional bias may not be relevant at the pre feasibility stage. However, as soon as you introduce any economic or technical parameters which entail selection, the conditional bias makes its appearance. In every project I have worked on, from pre-feasibility onwards, I have been asked for a grade/tonnage calculation - no matter how hand-waving it may be. The grade/tonnage curve will be affected by the conditional bias. By how much has to be assessed at the time. Most of Chapter 3 in Practical Geostatistics 1979 is devoted to working out what the (theoretical) global grade tonnage curve looks like when you adjust for the variance reduction. Even this will differ from the curve derived from the kriged estimates, no matter what size the block. The problem is even greater for environmental applications, especially toxic level risks. A 'global view' - i.e. a map - will not identify the true peaks because of the conditional bias. The fact that the overall average is unbiassed is irrelevant when trying to identify an area which is likely to be lethal. So, there is no contradiction. Conditional bias is unimportant (or irrelevant) until you apply some selection criterion. Yes, we agree. However, selection criteria can be relevant at very early stages of a project. It depends on your objective. Isobel http://uk.geocities.com/drisobelclark/practica.htm for free downloads of Practical Geostatistics 1979 PS: sorry I mis-spelled your name, I know it drives me nuts when people call me 'Clarke' ;-) ___ALL-NEW Yahoo! Messenger - so many all-new ways to express yourself http://uk.messenger.yahoo.com * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] spatial relationships
Mark I could not agree more with Gregoire (with one proviso, see below). Both geostatistics and any weighted average estimators are based on the same assumptions -- that relationship between values at two locations depends on the distance between them and (possibly) their relative orientation. If you cannot get a decent semi-variogram after trying every type of graph [normal, robust, relative] and every transformation and/or interpretation of your data [logarithm, indicator, rank transforms, Normal scores, mixed populations], you do not have a distance-based relationship. This conclusion also rules out: inverse distance weighting of any kind; Delaunay triangles; Thiessen polygons and so on. My proviso: there are other forms of spatial relationship than pure distance/direction types. The simplest example of this is data with a trend, where the value at a specified point will depend on its absolute position. There may be an added component for the 'residuals' which turns out to be distance/direction based. There are also many examples where, for example, flow characteristics, connectivity and so on play a large part in the structure of your variable. In short: no decent semi-variogram does NOT mean no spatial relationship. It means no simple second-order stationary geostatistical type spatial relationship. Isobel http://geoecosse.bizland.com/whatsnew.htm ___ALL-NEW Yahoo! Messenger - all new features - even more fun! http://uk.messenger.yahoo.com * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] spatial relationships
Dear oh Dear, I am failing to communicate (again). As far as I know, I didn't say you could not use geostatistics when a trend is present! I regularly use Universal Kriging for data with a trend and kriging with an external drift when the trend is governed by an outside factor (see free tutorial at website). The question originally posed what how does one decide that geostatistics is not appriate. The answer Gregoire and myself gave was when you cannot get a semi-variogam graph after trying all possible variations of transforms, interpretation and de-trending. I recently worked with an orange grove in Florida (bugs on oranges) which showed no decent semi-variogram even though rough inverse distance maps looked reasonable. It turned out they had two different kinds of tree in the orchard. Separating the 'rootstocks' yielded a vastly improved semi-variogram and decent geostatistical analysis. My additional point was that failure to obtain a semi-variogram model simply means that there is no 'distance related' structure. It does NOT mean there is NO spatial structure. Isobel http://geoecosse.bizland.com/softwares ___ALL-NEW Yahoo! Messenger - all new features - even more fun! http://uk.messenger.yahoo.com * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] Re: Frightened of Spatial Autocorrelation
Kevin Sounds like an ideal case for Geographically Weighted Regression. You could use semi-variograms or spatial auto-correlation to determine exactly how proximity defines relationship. My only current beef with GWR is the seemingly pre-defined distance weighting functions. Not had much time to get into this yet, so don't dump on me all you experts out there. I would be interested in any published results on this as one of my business partners is doing similar work on bronze age denmark. Isobel http://uk.geocities.com/drisobelclark ___ALL-NEW Yahoo! Messenger - all new features - even more fun! http://uk.messenger.yahoo.com * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
Re: [ai-geostats] A question on lag class and lag distance
xhy your questions are long-standing and as yet unanswered in general. 1. How to select the lag class and lag distance in order to obtain a more reasonable experimental variogram? I always think of it as focussing a camera. Believe there is a pattern in your data and our task is to balance 'width of interval' versus 'number of pairs in interval' to get the clearest picture. One of the things I have found most useful with irregularly spaced data is a 'nearest neighbour' analysis. Take each sample and find the closest one to it. Record the distance. Repeat for all samples. This process takes twice as long as calculating the semi-variogram but gives you an idea of the 'natural' or model spacing between your samples. This can be used to guide your choice of interval. Check out our free tutorial downloads at http://geoecosse.bizland.com/softwares 2. Is it reasonable to use an uneven set of lag (e.g. the lag increments are: 0-2.5m, 2.5-5.0m, 5.0-12.0m, 12.0-19.5m, 19.5-27.0m, 27.0-30.0m, 30.0-40m, 40-50m etc.) if a more stable variogram can be obtained? I am not sure I have ever seen this done, but don't see why not if you plot the point at the centre of gravity of your interval (i.e. average distance of pairs found). Hope this helps Isobel http://geoecosse.bizland.com/books.htm ___ALL-NEW Yahoo! Messenger - all new features - even more fun! http://uk.messenger.yahoo.com * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] Re: Sample data sets
Mark We have about 13 data sets available on our free download site, ranging from mining data to fisheries, agriculture and environmental stuff. Number of data ranges from 27 to 20,000. Download from http://geoecosse.bizland.com/softwares and find details and references for most of them at http://geoecosse.bizland.com/bookbits/Chapter1_PG2000.pdf Isobel ___ALL-NEW Yahoo! Messenger - all new features - even more fun! http://uk.messenger.yahoo.com * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] Re: regularization
Samuel Practical Geostatistics (1979) Chapter 3. Get it for free at http://uk.geocities.com/drisobelclark/practica.htm Isobel http://geoecosse.bizland.com/books.htm * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
Re: [ai-geostats] problem of spatial continuity of groundwater head
Kai I would suggest you take a look at: Introduction to Geostatistics: Applications in Hydrogeology (Stanford-Cambridge Program) P. K. Kitanidis which is a great base to work from. Isobel http:///geoecosse.bizland.com * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] F and T-test for samples drawn from the same p
Don Thank you for the extended clarification of F and t hypothesis test. For those unfamiliar with the concept, it is worth noting that the F test for multiple means may be more familiar under the title Analysis of variance. My own brief answer was in the context of Colin's question, where it was quite clear that he was talking aboutthe simplest F variance-ratio and t comparison of means test. Isobel * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] RE: F and T-test for samples drawn from the same p
Hence my recommendation to use cross cross validation Isobel http://geoecosse.bizland.com/books.htm --- Colin Daly [EMAIL PROTECTED] wrote: Hi Sorry to repeat myself - but the samples are not independent. Independance is a fundamental assumption of these types of tests - and you cannot interpret the tests if this assumption is violated. In the situation where spatial correlation exists, the true standard error is nothing like as small as the (s/sqrt(n)) that Chaosheng discusses - because the sqrt(n) depends on independence. Again, as I said before, if the data has any type of trend in it, then it is completely meaningless to try and use these tests - and with no trend but some 'ordinary' correlation, you must find a means of taking the data redundancy into account or risk get hopelessly pessimistic results (in the sense of rejecting the null hypothesis of equal means far too often) Consider a trivial example. A one dimensional random function which takes constant values over intervals of lenght one - so, it takes the value a_0 in the interval [0,1[ then the value a_1 in the interval [1,2[ and so on (let us suppose that each a_n term is drawn at random from a gaussian distribution with the same mean and variance for example). Next suppose you are given samples on the interval [0,2]. You spot that there seems to be a jump between [0,1[ and [1,2[ - so you test for the difference in the means. If you apply an f test you will easily find that the mean differs (and more convincingly the more samples you have drawn!). However by construction of the random function, the mean is not different. We have been lulled into the false conclusion of differing means by assuming that all our data are independent. Regards Colin Daly -Original Message- From: Chaosheng Zhang [mailto:[EMAIL PROTECTED] Sent: Sun 12/5/2004 11:42 AM To: [EMAIL PROTECTED] Cc: Colin Badenhorst; Isobel Clark; Donald E. Myers Subject: Re: [ai-geostats] F and T-test for samples drawn from the same p Dear all, I'm wondering if sample size (number of samples, n) is playing a role here. Since Colin is using Excel to analyse several thousand samples, I have checked the functions of t-tests in Excel. In the Data Analysis Tools help, a function is provided for t-Test: Two-Sample Assuming Unequal Variances analysis. This function is the same as those from many text books (There are other forms of the function). Unfortunately, I cannot find the function for assuming equal variances in Excel, but I assume they are similar, and should be the same as those from some text books. From the function, you can find that when the sample size is large you always get a large t value. When sample size is large enough, even slight differences between the mean values of two data sets (x bar and y bar) can be detected, and this will result in rejection of the null hypothesis. This is in fact quite reasonable. When the sample size is large, you are confident with the mean values (Central Limit Theorem), with a very small stand error (s/(sqrt(n)). Therefore, you are confident to detect the differences between the two data sets. Even though there is only a slight difference, you can still say, yes, they are significantly different. If you still remember some time ago, we had a discussion on large sample size problem for tests for normality. When the sample size is large enough, the result can always be expected (for real data sets), that is, rejection of the null hypothesis. Cheers, Chaosheng -- Dr. Chaosheng Zhang Lecturer in GIS Department of Geography National University of Ireland, Galway IRELAND Tel: +353-91-524411 x 2375 Direct Tel: +353-91-49 2375 Fax: +353-91-525700 E-mail: [EMAIL PROTECTED] Web 1: www.nuigalway.ie/geography/zhang.html Web 2: www.nuigalway.ie/geography/gis/index.htm - Original Message - From: Isobel Clark [EMAIL PROTECTED] To: Donald E. Myers [EMAIL PROTECTED] Cc: Colin Badenhorst [EMAIL PROTECTED]; [EMAIL PROTECTED] Sent: Saturday, December 04, 2004 11:49 AM Subject: [ai-geostats] F and T-test for samples drawn from the same p Don Thank you for the extended clarification of F and t hypothesis test. For those unfamiliar with the concept, it is worth noting that the F test for multiple means may be more familiar under the title Analysis of variance. My own brief answer was in the context of Colin's question, where it was quite clear that he was talking aboutthe simplest F variance-ratio and t comparison of means test. Isobel
Re: [ai-geostats] Re: F and T-test for samples drawn from the same p
Digby I see where you are coming from on this, but in fact the sill is composed of those pairs of samples which are independent of one another - or, at least, have reached some background correlation. This is why the sill makes a better estimate of the variance than the conventional statistical measures, since it is based on independent sampling. Isobel http://geoecosse.bizland.com/whatsnew.htm --- Digby Millikan [EMAIL PROTECTED] wrote: While your talking about sill's being the global variance which I read everywhere, isn't the global variance actually slightly less than the sill, as the values below the range of the variogram are not included? i.e. the sill would be the global variance when you have pure nugget effect. * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] Sill versus least-squares classical variance estimate
Meng-Ying We are talking about estimating the variance of a set of samples where spatial dependence exists. The classical statistical unbiassed estimator of the population variance is s-squared which is the sum of the squared deviations from the mean divided by the relevant degrees of freedom. If the samples are not inter-correlated, the relevant degrees of freedom are (n-1). This gives the formula you find in any introductory statistics book or course. If samples are not independent of one another, the degrees of freedom issue becomes a problem and the classical estimator will be biassed (generally too small on average). In theory, pairs of samples beyond the range of influence on a semi-variogram graph are independent of one another. In theory, the variance of the difference betwen two values which are uncorrelated is twice the variance of one sample around the population mean. This is thought to be why Matheron defined the semi-variogram (one-half the squared difference) so that the final sill would be (theoretically) equal to the population variance. There are computer software packages which will draw a line on your experimental semi-variogram at the height equivalent to the classically calculated sample variance. Some people try to force their semi-variogram models to go through this line. This is dumb as the experimental sill is a better estimate because it does have the degrees of freedom it is supposed to have. I am not sure whether this is clear enough. If you email me off the list, I can recommend publications which might help you out. Isobel http://geoecosse.bizland.com/books.htm --- Meng-Ying Li [EMAIL PROTECTED] wrote: Hi Isobel, Could you explain why it would be a better estimate of the variance when independance is considered? I'd rather think that we consider the dependance when the overall variance are to be estimated-- if there actually is dependance between values. Or are you talking about modeling sill value by the stablizing tail on the experimental variogram, instead of modeling by the calculated overall variance? Or, are we talking about variance of different definitions? I'd be concerned if I missed some point of the original definition for variances, like, the variance should be defined with no dependance beween values or something like that. Frankly, I don't think I took the definition of variance too serious when I was learning stats. Meng-ying Digby I see where you are coming from on this, but in fact the sill is composed of those pairs of samples which are independent of one another - or, at least, have reached some background correlation. This is why the sill makes a better estimate of the variance than the conventional statistical measures, since it is based on independent sampling. Isobel * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] variogram analysis
Rajive I haven't read the other responses yet, so this may be redundant. Two possibilities: (1) anisotropy: if this is shallow marine data there should be a difference between longshore drift and off-shore deepening of sea-bed. You have an omni-directional semi-variogram. It is possible that the sampling grid is irregular enough to be highlighting directional differences?? (2) mega-ripples: I have seen similar behaviour in off-shore marine diamonds which tend to hug the bottom of trenches or ripples. Major ocean beds have mega-ripples on the kilometre scale, which is what you are seeing here. More worrying, I would say, is the fact that your graph is dropping with distance. This suggests that you also have some underlying trend (non-stationarity) which is causing closely spaced samples to be 'more different' than those further apart. I notice you are using a log transform. What does your probability plot look like? Isobel * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] Re: Sill versus least-squares classical variance estimate
Meng-Ying No, I do not think we are communicating. The variance of data values is not affected by correlation between the sample values. The estimated variance for the population IS affected by correlation between the sample values. Statistical inference about the population is based on the assumption that samples were taken randomly and independently from that population. It is the process of estimation of unknown parameters by classical statistical theory which requires these assumptions. Geostatistical inference does not require absence of correlation, quite the contrary. The semi-variogram graph is constructed on the assumption that there is a correlation between samples and that this depends on distance and direction between the pair of samples. If we have a stationary situation, where the mean and variance are constant over the study area, the semi-variogram generally reaches a sill value. The distance at which this happens is interpreted as that distance beyond which the correlation is zero. Sample pairs at this distance or greater can be used to estimate the variance, since the statistical assumptions are now satisifed. Isobel http://geoecosse.bizland.com/whatsnew.htm --- Meng-Ying Li [EMAIL PROTECTED] wrote: Hi Isobel, I understand all points you pointed out, but I'm not sure why the variance should be defined as data NOT SPATIALLY CORRELATED when they may or may not be correlated. Thanks for the clarification, though, I don't think I'd be able to clarify the things you clarifies. You're good. Meng-ying On Wed, 8 Dec 2004, Isobel Clark wrote: Meng-Ying I don't know how to say this any other way. At distances larger than the range of influence, samples are NOT SPATIALLY CORRELATED. The variance of the difference between two uncorrelated samples is twice the variance of one sample around the mean. The semi-variogram is one-half of the variance of the difference. Hence the sill is (theoretically) equal to the variance. The sill is based on all pairs of samples found at a distance greater thn the range of influence. The classical statistical estimator of the variance is only unbiassed if the correct degrees of freedom are used. If the samples are correlated, n-1 is NOT the correct degrees of freedom. All explained in immense detail in Practical Geostatistics 2000, Clark and Harper, http://geoecosse.hypermart.net Did I get it clear this time? Isobel --- Meng-Ying Li [EMAIL PROTECTED] wrote: I understand why it is not appropriate to force the sill so it matches the sample variance. My question is, why estimate the overall variance by the sill value when data are actually correlated? Meng-ying On Tue, 7 Dec 2004, Isobel Clark wrote: Meng-Ying We are talking about estimating the variance of a set of samples where spatial dependence exists. The classical statistical unbiassed estimator of the population variance is s-squared which is the sum of the squared deviations from the mean divided by the relevant degrees of freedom. If the samples are not inter-correlated, the relevant degrees of freedom are (n-1). This gives the formula you find in any introductory statistics book or course. If samples are not independent of one another, the degrees of freedom issue becomes a problem and the classical estimator will be biassed (generally too small on average). In theory, pairs of samples beyond the range of influence on a semi-variogram graph are independent of one another. In theory, the variance of the difference betwen two values which are uncorrelated is twice the variance of one sample around the population mean. This is thought to be why Matheron defined the semi-variogram (one-half the squared difference) so that the final sill would be (theoretically) equal to the population variance. There are computer software packages which will draw a line on your experimental semi-variogram at the height equivalent to the classically calculated sample variance. Some people try to force their semi-variogram models to go through this line. This is dumb as the experimental sill is a better estimate because it does have the degrees of freedom it is supposed to have. I am not sure whether this is clear enough. If you email me off the list, I can recommend publications which might help you out. Isobel http://geoecosse.bizland.com/books.htm --- Meng-Ying Li [EMAIL PROTECTED] wrote: Hi Isobel, Could you explain why it would be a better estimate of the variance when independance is considered? I'd rather think that we consider the dependance when the overall variance are to be estimated
[ai-geostats] descriptive statistics or inference?
And just a personal opinion, I would like to think geostatistic theories apply to population of any size, as small as 27, or as large as 1,000,000. If I'm making an example that geostatistics doesn't apply, then there's something to concern about in this approach. Geostatistics applies to any size of sample set but for the theory to work ou have to have a relatively enormous population to draw rom. Put in plain terms, the assumption is that the withdrawal of the samples does not materially affect the behaviour of the population. If you have the whole population, you don't need to do tests or estimates. Isobel http:geoecosse.bizland.com/books.htm * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] within line variance
Meng-Ying Assuming that you generated your line with a Spherical model, range 3, 27 samples making 9 ranges the variance within that line will (theoretically) be 0.9191 of the semi-variogram sill. Of course this theory depends on you have every possible sample in that length, not just 27 of them. Isobel http://uk.geocities.com/drisobelclark/practica.htm * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
