Model-based Geostatistics

(to be presented in the 14° SINAPE, 24-28 July 2000, Caxambu, MG, Brasil)

Peter J. Diggle
Lancaster University, UK
p.diggle@lancaster.ac.uk

Paulo J. Ribeiro Jr.
Universidade Federal do Paraná, Brasil
paulojus@est.ufpr.br


Contact address: Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, UK.

PREFACE

Geostatistics has an interesting history. Originally, the term was coined by Georges Mathéron and colleagues at Fontainebleau, France, to describe their work addressing problems of spatial prediction arising in the mining industry. The ideas of the Fontainebleau school were developed largely independently of the mainstream of spatial statistics, with a distinctive terminology and style. This tended to conceal the strong connections with parallel developments in spatial statistics by Matérn, whose Swedish doctoral thesis published in 1960 is still widely cited, Whittle, Bartlett and others. For example, the core geostatistical method known as kriging is equivalent to minimum mean square error prediction under a linear Gaussian model. Brian Ripley's first book on spatial statistics (Ripley, 1981) made the connection explicit. Ten years later, Noel Cressie's much larger book (Cressie, 1991) considered geostatistics to be one of three main branches of spatial statistics, the others being discrete spatial variation (distributions on lattices, Markov random fields,...) and spatial point processes. Geostatistical methods are now used in many areas of application, far beyond the mining context in which they were originally developed.

Despite this apparent integration with spatial statistics, geostatistical practice still reflects its independent origins, and our view is that this has some undesirable consequences. In particular, geostatistical inference is often ad hoc in nature, with explicit stochastic models rarely declared and, consequently, little use made of the likelihood-based methods of inference which are central to modern statistics.

Diggle, Moyeed and Tawn (1998) used the phrase model-based geostatistics to describe an approach to geostatistical problems based on the application of formal statistical methods under an explicitly assumed stochastic model. This course takes the same point of view.

The course is an applied statistical counterpart to Michael Stein's excellent book (Stein, 1999), which gives a rigorous mathematical theory of kriging.

We illustrate the methodology by applying it to real data-sets. We have written a library (geoS) of S-PLUS functions, and its R counterpart (geoR) to implement the methods described in the course. This software, together with the data-sets used in the course, is freely available from the web-address:
http://www.maths.lancs.ac.uk/~diggle

Finally, we thank ABE (Associação Brasileira de Estatística) for the opportunity to present our ideas at the 14° SINAPE and our colleagues in Lancaster, UK for their helpful input. We particularly thank Laura Regina Bernardes Kiihl (Instituto Agronõomico do Paranáa, Londrina, Brazil) for providing the Paraná rainfall data, and Dr Steve Simon for providing the Rongelap residual contamination data. PJD acknowledges financial support from the UK Engineering and Physical Sciences Research Council (Grant number GL/L56206) and from the European Commission (TMR Network in Spatial and Computational Statistics). These notes were written during the second author's PhD program at the Department of Mathematics and Statistics, Lancaster University, UK. PJRJr acknowledges financial support from CAPES/Brasil (Grant number BEX 1676/96-2) and Universidade Federal do Paraná.

Course transparencies

The course slides are available for download in 2 different formats: compressed postscript (.ps.gz) or pdf format. Select one of the options below.
  1. pdf format
    This file can be visualised using the Adobe Acrobat reader

  2. Compressed postscript format.
    For files in this format you will need to (i) download one of the files below; (ii) uncompress it using Winzip (Windows) or gunzip (Linux/Unix) (iii) visualize and /or send to the printer using ghostview.

Notes for the geoR/geoS tutorial

The tutorial session will be based on a Tecnical Report describing the software, available in compressed postscript (.ps.gz) or pdf format. Select one of the options below for download.
  1. pdf format
    This file can be visualised using the Adobe Acrobat reader

  2. Compressed postscript format.
    For files in this format you will need to (i) download one of the files below; (ii) uncompress it using Winzip (Windows) or gunzip (Linux/Unix) (iii) visualize and /or send to the printer using ghostview.

go to geoR/geoS home page

go to Something about geostatistics home page

go to 14°SINAPE home page

http://www.maths.lancs.ac.uk/~ribeiro/
Last modified: Mon Jun 26 15:14:40 BST 2000