kriging
Dear Frede I would not say that the methods discussed in the MBG book should be refered as "regression kriging". As far as I understand, the term "regression kriging", despite of all variations, refer to proposals/algorithms for which predictions are obtained combining two stages: 1. get predictions by some method (linear model, GLM, GAM, trees, etc) without accounting for the spatial correlations by a stochastic mechanism, without assuming a random field 2. either use or combine the above with some sort of kriging, i.e., spatial predictions assuming and using the spatial covariance structure This brings issue on how to assess prediction variances and so on. The algorithms in geoR and geoRglm **does not** follow this kind of two stage route. **Given the assumed model**, the inference and prediction follows from it and therefore likelihood based methods (including Bayesian) can be adopted. This does come with some price --- As Edzer already pointed, for very large number of data points this can be prohibitive for dealing with large covariance matrices and this is a limitation of geoR/geoRglm. There are possible workarounds still within the same paradigma but not (yet?) implemented in such packages best P.J. Paulo Justiniano Ribeiro Jr LEG (Laboratorio de Estatistica e Geoinformacao) Universidade Federal do Parana Caixa Postal 19.081 CEP 81.531-990 Curitiba, PR - Brasil Tel: (+55) 41 3361 3573 Fax: (+55) 41 3361 3141 e-mail: paulojus AT ufpr br http://www.leg.ufpr.br/~paulojus
On Fri, 4 Jul 2008, Frede Aakmann T?gersen wrote:
Sorry for dropping in late in this thread, which I have not followed closely. Perhaps Paulo Ribeiro can correct me but thinking of geostatistics in terms of statistical models then I think that the book by Diggle & Ribeiro: http://www.springer.com/geosciences/computer+&+mathematical+applications/book/978-0-387-32907-9 would give some regular methods to do what some call regression kriging (and related methods) based on statistical models. I know this requires some distributional assumptions, but there are straight forward methods for Gaussian data as well as data with more general distribution as in "generalized linear models". Also moderate departure from the assumption of Gaussian data do not have that big effect on inferences in such models. The above reference is supporting the geoR package in R. Med venlig hilsen / Regards Frede Aakmann T?gersen Forsker / Scientist AARHUS UNIVERSITET / UNIVERSITY OF AARHUS Det Jordbrugsvidenskabelige Fakultet / Faculty of Agricultural Sciences Inst. for Genetik og Bioteknologi / Dept. of Genetics and Biotechnology Blichers All? 20, P.O. BOX 50 DK-8830 Tjele Tel: +45 8999 1900 Direct: +45 8999 1878 Mobile: +45 E-mail: FredeA.Togersen at agrsci.dk <mailto:FredeA.Togersen at agrsci.dk> Web: www.agrsci.dk <https://djfpost.agrsci.dk/exchweb/bin/redir.asp?URL=http://www.agrsci.dk/>
________________________________ DJF udbyder nye uddannelser <https://djfpost.agrsci.dk/exchweb/bin/redir.asp?URL=http://www.agrsci.dk/ny_navigation/uddannelse/> / DJF now offers new degree programmes <https://djfpost.agrsci.dk/exchweb/bin/redir.asp?URL=http://www.agrsci.org/content/view/full/34133> . Tilmeld dig DJF's nyhedsbrev / Subscribe Faculty of Agricultural Sciences Newsletter <https://djfpost.agrsci.dk/exchweb/bin/redir.asp?URL=http://www.agrsci.dk/user/register?lan=dan-DK> . Denne email kan indeholde fortrolig information. Enhver brug eller offentligg?relse af denne email uden skriftlig tilladelse fra DJF er ikke tilladt. Hvis De ikke er den tilt?nkte adressat, bedes De venligst straks underrette DJF samt slette emailen. This email may contain information that is confidential. Any use or publication of this email without written permission from Faculty of Agricultural Sciences is not allowed. If you are not the intended recipient, please notify Faculty of Agricultural Sciences immediately and delete this email. ________________________________ Fra: r-sig-geo-bounces at stat.math.ethz.ch p? vegne af Edzer Pebesma Sendt: to 03-07-2008 13:33 Til: Hengl, T. Cc: r-sig-geo at stat.math.ethz.ch; Dave Depew Emne: Re: [R-sig-Geo] kriging Hengl, T. wrote: I agree with Paulo - gstat can work with any linear model including the transforms of the original predictors e.g.: Z ~ X + X^2 + Y + Y^2 etc. The problem is that gstat implements the so-called Kriging-with-external-trend algorithm to make predictions (see section 2.1 of my lecture notes), which is mathematically more elegant, but then it accepts only a family of linear models (and not GLMs, regreesion-trees etc.). I have been promoting the concept of regression-kriging (deterministic and stochastic predictions seperated), but we still did not implement it in any package so far. And I can see why, as there are quite a few problems still to solve (afaik) ahead of you. When you cut the problem in two, do the regression estimation and residual prediction in two separate processes (often under different assumptions, e.g. wrt spatial correlation) you ignore the correlation between the two. Finding a prediction variance by naively adding the variances of the two components e.g. does not yield zero variance at observation locations, because a non-zero correlation is ignored. At other locations, this correlation is also non-zero. Furthermore, if you cut the problem in two for e.g. binomial or Poisson distributed cases, in this approach you likely end up with negative predictions or predictions above one for the binomial case. Does the paper you refer to (by yourself) give solutions to these two problems? You can at any time separate the predictions (e.g. krige only the residuals), but then gstat will not give you the regression-kriging variance, and you can not run geostatistical simulations. No, of course not, for the reasons mentioned above. The gstat approach is: if you want to make a mess, please take responsibility for it by yourself (and don't blame me--through the package). There is a paper I did it with count data, though, which is E.J. Pebesma, R.N.M. Duin, P.A. Burrough, 2005. Mapping Sea Bird Densities over the North Sea: Spatially Aggregated Estimates and Temporal Changes. Environmetrics 16 <http://www3.interscience.wiley.com/cgi-bin/jissue/110577560>, (6), p 573-587 <http://dx.doi.org/10.1002/env.723>. and (part of) the analysis is found in library(gstat) demo(fulmar) I'm also confused by this term "regression kriging". Would you claim that the universal kriging/kriging with (one or more) external drifts implemented by gstat is not regression kriging? Are you actually working on a package that does do regression kriging as you define it? -- Edzer see also: https://stat.ethz.ch/pipermail/r-sig-geo/2008-February/003174.html All the best, Tom Hengl http://spatial-analyst.net <http://spatial-analyst.net/> Hengl, T., 2007. A Practical Guide to Geostatistical Mapping of Environmental Variables. EUR 22904 EN Scientific and Technical Research series, Office for Official Publications of the European Communities, Luxemburg, 143 pp. http://bookshop.europa.eu/uri?target=EUB:NOTICE:LBNA22904:EN:HTML -----Original Message----- From: r-sig-geo-bounces at stat.math.ethz.ch on behalf of Dave Depew Sent: Mon 6/16/2008 10:54 PM To: Paulo Justiniano Ribeiro Jr Cc: r-sig-geo at stat.math.ethz.ch Subject: Re: [R-sig-Geo] kriging Ok, What about higher order polynomials? I have fitted one using a gam to the data which which helps to normalize the residuals, and reduce the variance of the residuals. Is it simply a matter of plugging in the function into the gstat command line? Or is it simpler to krig the residuals and then add the trend back to the interpolated residual grid? Paulo Justiniano Ribeiro Jr wrote: Dave, what is necessary for UK is a relation expressed by a linear model, not necessaraly a linear relation between the variables. e.g. you could have a second degree polinomial and still work within the scope of universal kriging. On Mon, 16 Jun 2008, Dave Depew wrote: Hi all, I have a data set that I would like to krige to interpolate between transects. There is a non-linear trend between two of the variables...my impression from reading the gstat help file is that there must be a linear relationship between the data to use universal kriging? Second, would a method of non-linear regression followed by modelling of the residuals with a semivariogram be an appropriate solution? Thanks, Dave _______________________________________________ R-sig-Geo mailing list R-sig-Geo at stat.math.ethz.ch https://stat.ethz.ch/mailman/listinfo/r-sig-geo Paulo Justiniano Ribeiro Jr LEG (Laboratorio de Estatistica e Geoinformacao) Universidade Federal do Parana Caixa Postal 19.081 CEP 81.531-990 Curitiba, PR - Brasil Tel: (+55) 41 3361 3573 Fax: (+55) 41 3361 3141 e-mail: paulojus AT ufpr br http://www.leg.ufpr.br/~paulojus _______________________________________________ R-sig-Geo mailing list R-sig-Geo at stat.math.ethz.ch https://stat.ethz.ch/mailman/listinfo/r-sig-geo [[alternative HTML version deleted]] _______________________________________________ R-sig-Geo mailing list R-sig-Geo at stat.math.ethz.ch https://stat.ethz.ch/mailman/listinfo/r-sig-geo -- Edzer Pebesma Institute for Geoinformatics (IfGI) University of M?nster http://ifgi.uni-muenster.de/ [[alternative HTML version deleted]]