Pierre Goovaerts
Fri, 29 Sep 2006 12:27:41 -0700
Hello, I have discussed the use of stochastic simulation and kriging to model local versus spatial uncertainty in the following paper: Goovaerts, P. 2001. Geostatistical modelling of uncertainty in soil science. Geoderma, 103: 3-26. <http://www.terraseer.com/training/geostats/geoder01.pdf> As Ashton pointed out, stochastic simulation is now trendy and several times I came across papers where the authors spent a great deal of time generating a bunch of realizations before simply taking the average of all the maps.. which is clearly a waste of CPU time and memory... As Edzer mentioned, the mean and variance of Gaussian simulated values will give back the kriging estimate and variance. This is, however, not the case if the sample histogram is asymmetric and data need to be normal score transformed... You can still use multiGaussian kriging but the derivation of the kriging estimate and variance in the original space needs some work (see Saito, H. and P. Goovaerts. 2000. Geostatistical <http://home.att.ne.jp/grape/geostat/PAPER/EST01.pdf> interpolation of positively skewed and censored data in a dioxin contaminated site. Environmental Science & Technology, vol.34, No.19: 4228-4235. ), In this case, it is usually more straightforward for users with no coding skill to generate a bunch of realizations and compute statistics from the set of back-transformed simulated values. In general, stochastic simulation is useful to model uncertainty over spatial supports that are larger than the measurement support (i.e. upscaling), as well as to characterize the uncertainty prevailing at several locations simultaneously (e.g. uncertainty about the occurrence of a string of low or high values). Edzer made a good point that the kriging variance is derived from a model, and we shouldn't blame the variance as an inadequate measure of uncertainty whenever we use a model that is inappropriate for our data... On the other hand, the kriging variance has too often been portrayed as the magic recipe that will reveal where to collect additional samples.. while it simply tells you to sample in sparsely sampled areas... Pierre Pierre Goovaerts Chief Scientist at BioMedware Inc. Courtesy Associate Professor, University of Florida President of PGeostat LLC Office address: 516 North State Street Ann Arbor, MI 48104 Voice: (734) 913-1098 (ext. 8) Fax: (734) 913-2201 http://home.comcast.net/~goovaerts/ ________________________________ From: [EMAIL PROTECTED] on behalf of Ashton Shortridge Sent: Fri 9/29/2006 12:47 PM To: Edzer J. Pebesma Cc: Gustavo G. Pilger; Kerry Ritter; ai-geostats@jrc.it Subject: Re: AI-GEOSTATS: kriging variance and accuracy My own take differs a bit from Edzer's. He is of course correct that the use of conditional simulation to identify uncertainty at a location is at best an inefficient way to accomplish this. I've reviewed articles that did this. I don't know if it's ignorance or just the trendy nature of simulation. However, if one's application is concerned with joint uncertainties, for example, the joint probability that an entire region is above a certain height, than simulation appears to be necessary. Yours, Ashton Shortridge On Friday 29 September 2006 11:12 am, Edzer J. Pebesma wrote: > Dear Kerry and Gustavo, > > The kriging variance is a perfect measure for estimation uncertainty as > long as a second order stationary model is a good representation of the > data under study. Obviously, if variability and/or spatial correlation > varies over the field of interest and you have sufficient data to > characterize this, or e.g. do a non-linear transform such as a > log-transform to correct for a proportional effect, than you can and > will do better when taking this into account. > > In my opinion papers such as those by Journel and Rossi have > over-shouted their point, and have ignored that for many cases a second > order stationary random field is a suitable model, if not the only > possible. > > The argument that after rejecting the kriging variance, conditional > simulation is suddenly needed as the solution get some measure of > uncertainty is invalid: if you create a large enough set of conditional > Gaussian simulations, their mean value equals the kriging mean and their > variance equals the kriging variance. Nothing is gained, only an > expensive approximation of something rather cheap is obtained. > > You will not find many papers that make this point, as the only point is > that someone else is wrong. Not many people like to write such stuff. > Below is a reference that may be hard to get (but you can google for the > first author). I for instance didn't enjoy writing this email. > > Best regards, > -- > Edzer > > Heuvelink, G.B.M. and E.J. Pebesma, 2002, Is the ordinary kriging > variance a proper measure of interpolation error? In: Proceedings of the > fifth International Symposium on Spatial Accuracy Assessment in Natural > Resources and Environmental Sciences (eds. G. Hunter and K. Lowell). > Melbourne: RMIT University, 179-186. > > Gustavo G. Pilger wrote: > > Hi, > > > > Indeed the kriging variance is only semi-variogram and spatial data > > configuration dependent. The kriging variance is calculated taking > > into account only the geometry of the samples, i.e. their spatial > > arrangement and the semi-variogram. Basically, kriging variance do not > > take into account the value of the samples, but only their location > > (and the semi-variogram), consequently ignoring the local variability. > > Therefore this parameter is not appropriate to measure uncertainty. > > For this purpose you should consider the use of conditional simulation > > methods. > > > > I wrote some papers about this subject some years ago. For exemple: > > > > PILGER, Gustavo G.; COSTA, Joao Felipe Coimbra Leite; KOPPE, Jair > > Carlos, 2001. Additional Samples: Where they Should be Located?. > > Natural Resources Research, New York, v. 10, n. 3, p. 197-207. > > > > I can send you a copy if you wish. > > > > I hope this helps you. > > > > Cheers. > > <><><><><><><><><><><><><><><><><><><><><><><> > > Gustavo G. Pilger, Mining Engineer, MSc, PhD > > Senior Geostatistician > > MBR - Brazil > > <><><><><><><><><><><><><><><><><><><><><><><> > > > >> Hi. I just read through Journel and Rossi's 1999 paper, "When do we > >> need a trend model in Kriging". In the appendix they say "A kriging > >> variance is but a variogram-model dependent ranking of data > >> configurations; being data-value independent, it is generally not a > >> measure of local accuracy...This fact is unfortunately not yet fully > >> appreciated by some practitioners". Can someone explain the > >> implications of this in terms of determining cost-efficiency analysis > >> for sample designs? Specifically, can we use kriging variance > >> estimates across potential sampling grids, (from modeled variograms > >> estimated from say a pilot study) to estimate the variability > >> associated with different sampling densities/configurations. In > >> addition, can someone provide some references that address this topic. > >> > >> Thanks, > >> Kerry > >> + > >> + To post a message to the list, send it to ai-geostats@jrc.it > >> + To unsubscribe, send email to majordomo@ jrc.it with no subject and > >> "unsubscribe ai-geostats" in the message body. DO NOT SEND > >> Subscribe/Unsubscribe requests to the list > >> + As a general service to list users, please remember to post a summary > >> of any useful responses to your questions. > >> + Support to the forum can be found at http://www.ai-geostats.org/ > > > > + > > + To post a message to the list, send it to ai-geostats@jrc.it > > + To unsubscribe, send email to majordomo@ jrc.it with no subject and > > "unsubscribe ai-geostats" in the message body. DO NOT SEND > > Subscribe/Unsubscribe requests to the list > > + As a general service to list users, please remember to post a > > summary of any useful responses to your questions. > > + Support to the forum can be found at http://www.ai-geostats.org/ > > + > + To post a message to the list, send it to ai-geostats@jrc.it > + To unsubscribe, send email to majordomo@ jrc.it with no subject and > "unsubscribe ai-geostats" in the message body. DO NOT SEND > Subscribe/Unsubscribe requests to the list + As a general service to list > users, please remember to post a summary of any useful responses to your > questions. + Support to the forum can be found at > http://www.ai-geostats.org/ -- Ashton Shortridge Assistant Professor [EMAIL PROTECTED] Dept of Geography http://www.msu.edu/~ashton 235 Geography Building ph (517) 432-3561 Michigan State University fx (517) 432-1671 Geography Has moved! Map: http://www.rsgis.msu.edu/images/parking-map.gif + + To post a message to the list, send it to ai-geostats@jrc.it + To unsubscribe, send email to majordomo@ jrc.it with no subject and "unsubscribe ai-geostats" in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list + As a general service to list users, please remember to post a summary of any useful responses to your questions. + Support to the forum can be found at http://www.ai-geostats.org/ + + To post a message to the list, send it to ai-geostats@jrc.it + To unsubscribe, send email to majordomo@ jrc.it with no subject and "unsubscribe ai-geostats" in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list + As a general service to list users, please remember to post a summary of any useful responses to your questions. + Support to the forum can be found at http://www.ai-geostats.org/
