between wants and haves.
Happy New Year to everyone
Isobel Clark
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uch 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
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--- 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
s the semi-variogram fit to
the experimental with a weighted least squares.
Isobel Clark
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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
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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
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
boreholes.
Inferred: anything the geologist thinks is there.
Hope this helps.
Isobel Clark
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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
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
interesting. How do you define
better -- prettier? nicer? easier to interpret? less
polluted?
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widely applicable.
Is it a software limitation for the package mentioned?
Isobel Clark
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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.
. 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
. It is your voices we want to hear, not
us border line pensioners
Isobel Clark
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Thank you, Marco!
My point exactly.
Isobel
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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
round a few times as there is no guarantee
that the new set won't have negative weights
Isobel Clark
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or you can type
in data from the keyboard.
Comments and queries to me please.
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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
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
to your answers.
Isobel Clark
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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
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
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
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
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
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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
accordingly.
This is documented in Matheron's original works.
Isobel Clark
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as quickly as you can.
Nokia 5510 looks weird sounds great.
Go to http://uk.promotions.yahoo.com/nokia/ discover
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
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--- 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
.
Isobel Clark
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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
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of influence and see if your answers
change.
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standards.
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sampled are 'some fish' areas and you just didn't
catch any.
Isobel Clark
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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
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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
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
. 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
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
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
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
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Russell
Absolutely on the spot.
We call this the 'ygiagam' criterion (your guess is as
good as mine) ;-)
Isobel Clark
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if you have a significant
replication variance.
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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
)
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
).
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
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
!
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
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.
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
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P and look for papers in the second
half of the 1990s).
Isobel Clark
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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
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
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
constant.
Isobel Clark
http://ecosse.ontheweb.com/whatsnew.htm
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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
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
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
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
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).
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]
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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
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
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
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
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
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
member of the list.
Isobel Clark
http://geoecosse.bizland.com/whatsnew.htm
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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
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
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
.
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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*
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
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(
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
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
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
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.
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
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
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
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
Digby
The variance/sill relationship is theoretical and does
not depend on the layout of the samples, regular or
clustered. Since the sill only uses pairs where
samples are uncorrelated from one another, the
clustering is irrelevant.
It does depend on the distribution of the samples
values being
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