Dear all, For those interested, I have asked Gregoire to put the paper that Edzer refers to on the ai-geostats documents section.
It was written in a time that the kriging variance was heavily attacked. We felt the need to react to the biased views expressed at the time. One interesting outcome of the paper is that it is not necessarily a good thing to let the measure for interpolation accuracy strongly depend on the degree of local spatial variation. Apparently, one can be too 'data-charged'! As usual, I agree with everything that Edzer writes. Gerard Gerard B.M. Heuvelink Environmental Sciences Group Wageningen University and Research Centre P.O. Box 47 6700 AA Wageningen The Netherlands tel +31 317 474628 / 485208 email [EMAIL PROTECTED] http://www.sil.wur.nl/UK/ -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Edzer J. Pebesma Sent: vrijdag 29 september 2006 17:13 To: Gustavo G. Pilger Cc: Kerry Ritter; ai-geostats@jrc.it Subject: Re: AI-GEOSTATS: kriging variance and accuracy 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. 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