Spatial statistics are useful in subjects as diverse as climatology,
ecology, economics, environmental and earth sciences, epidemiology,
image analysis and more. This book covers the best-known spatial models
for three types of spatial data: geostatistical data (stationarity,
intrinsic models, variograms, spatial regression and space-time models),
areal data (Gibbs-Markov fields and spatial auto-regression) and point
pattern data (Poisson, Cox, Gibbs and Markov point processes). The level
is relatively advanced, and the presentation concise but complete.
The most important statistical methods and their asymptotic properties
are described, including estimation in geostatistics, autocorrelation
and second-order statistics, maximum likelihood methods, approximate
inference using the pseudo-likelihood or Monte-Carlo simulations,
statistics for point processes and Bayesian hierarchical models. A
chapter is devoted to Markov Chain Monte Carlo simulation (Gibbs
sampler, Metropolis-Hastings algorithms and exact simulation).
A large number of real examples are studied with R, and each chapter
ends with a set of theoretical and applied exercises. While a foundation
in probability and mathematical statistics is assumed, three appendices
introduce some necessary background. The book is accessible to senior
undergraduate students with a solid math background and Ph.D. students
in statistics. Furthermore, experienced statisticians and researchers in
the above-mentioned fields will find the book valuable as a
mathematically sound reference.
This book is the English translation of Modélisation et Statistique
Spatiales published by Springer in the series Mathématiques &
Applications, a series established by Société de Mathématiques
Appliquées et Industrielles (SMAI).
