Basic Linear Geostatistics

Based on a postgraduate course that has been successfully taught for over 15 years, the underlying philosophy here is to give students an in-depth understanding of the relevant theory and how to put it into practice. This involves going into the theory in more detail than most books do, and also discussing its applications. It is assumed that readers, students and professionals alike are familiar with basic probability and statistics, as well as the matrix algebra needed for solving linear systems; however, some reminders on these are given in an appendix. Exercises are integrated throughout, and the appendix contains a review of the material.

This brief will provide a bridge in succinct form between the geostatistics textbooks and the computer manuals for `push-button' practice. It is becoming increasingly important for practitioners, especially neophytes, to understand what underlies modern geostatistics and the currently available software so that they can choose sensibly and draw correct conclusions from their analysis and mapping. The brief will contain some theory, but only that needed for practitioners to understand the essential steps in analyses. It will guide readers sequentially through the stages of properly designed sampling, exploratory data analysis, variography (computing the variogram and modelling it), followed by ordinary kriging and finally mapping kriged estimates and their errors. There will be short section on trend and universal kriging. Other types of kriging will be mentioned so that readers can delve further in the substantive literature to tackle more complex tasks.

An introduction to geostatistics stressing the multivariate aspects for scientists, engineers and statisticians. The book presents a brief review of statistical concepts, a detailed introduction to linear geostatistics, and an account of three basic methods of multivariate analysis. Applications from very different areas of science, as well as exercises with solutions, are provided to help convey the general ideas. In this second edition, the chapters regarding normal kriging and cokriging have been restructured and the section on non-stationary geostatistics has been entirely rewritten.

Introducing geostatistics from a multivariate perspective is the main aim of this book. The idea took root while teaching geostatistics at the Centre de Geostatis tique (Ecole des Mines de Paris) over the past ten years in the two postgraduate programs DEA and CFSG. A first script of lecture notes in French originated from this activity. A specialized course on Multivariate and Exploratory Geostatistics held in September 1993 in Paris (organized in collaboration with the Department of Statistics of Trinity College Dublin) was the occasion to test some of the mate rial on a pluridisciplinary audience. Another important opportunity arose last year when giving a lecture on Spatial Statistics during the summer term at the Department of Statistics of the University of Washington at Seattle, where part of this manuscript was distributed in an early version. Short accounts were also given during COMETT and TEMPUS courses on geostatistics for environment al studies in Fontainebleau, Freiberg, Rome and Prague, which were sponsored by the European Community. I wish to thank the participants of these various courses for their stimulating questions and comments. Among the organizers of these courses, I particularly want to acknowledge the support received from Georges Matheron, Pierre Chau vet, Margaret Armstrong, John Haslett and Paul Sampson. Michel Grzebyk has made valuable comments on Chapters 26 and 27, which partly summarize some of his contributions to the field.

Linear geostatistics is a fast developing field of research and its principles are extended over other fields of activity. Tools such as the variogram and kriging are now in everyday use for estimating the mean grade of material in an area from values achieved from measured samples. Non-linear geostatistics is at the fore-front of statistical development, it has a potential application over a wide range of practical problems and is likely to occupy an important place in the statutory monitoring and control of air, water, and land pollution. This book provides a comprehensive introduction to the field for geographers and engineers.

This fully revised third edition introduces geostatistics by emphasising the multivariate aspects for scientists, engineers and statisticians. Geostatistics offers a variety of models, methods and techniques for the analysis, estimation and display of multivariate data distributed in space or time. The text contains a brief review of statistical concepts, a detailed introduction to linear geostatistics, and an account of 3 basic methods of multivariate analysis. Applications from different areas of science, as well as exercises with solutions, are provided to help convey the general ideas. The introductory chapter has been divided into two separate sections for clarity. The final section deals with non-stationary geostatistics.

Model-based Geostatistics for Global Public Health: Methods and Applications provides an introductory account of model-based geostatistics, its implementation in open-source software and its application in public health research. In the public health problems that are the focus of this book, the authors describe and explain the pattern of spatial variation in a health outcome or exposure measurement of interest. Model-based geostatistics uses explicit probability models and established principles of statistical inference to address questions of this kind. Features: Presents state-of-the-art methods in model-based geostatistics. Discusses the application these methods some of the most challenging global public health problems including disease mapping, exposure mapping and environmental epidemiology. Describes exploratory methods for analysing geostatistical data, including: diagnostic checking of residuals standard linear and generalized linear models; variogram analysis; Gaussian process models and geostatistical design issues. Includes a range of more complex geostatistical problems where research is ongoing. All of the results in the book are reproducible using publicly available R code and data-sets, as well as a dedicated R package. This book has been written to be accessible not only to statisticians but also to students and researchers in the public health sciences. The Authors Peter Diggle is Distinguished University Professor of Statistics in the Faculty of Health and Medicine, Lancaster University. He also holds honorary positions at the Johns Hopkins University School of Public Health, Columbia University International Research Institute for Climate and Society, and Yale University School of Public Health. His research involves the development of statistical methods for analyzing spatial and longitudinal data and their applications in the biomedical and health sciences. Dr Emanuele Giorgi is a Lecturer in Biostatistics and member of the CHICAS research group at Lancaster University, where he formerly obtained a PhD in Statistics and Epidemiology in 2015. His research interests involve the development of novel geostatistical methods for disease mapping, with a special focus on malaria and other tropical diseases. In 2018, Dr Giorgi was awarded the Royal Statistical Society Research Prize "for outstanding published contribution at the interface of statistics and epidemiology." He is also the lead developer of PrevMap, an R package where all the methodology found in this book has been implemented.