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 Modelisation et Statistique Spatiales published by Springer in the series Mathematiques & Applications, a series established by Societe de Mathematiques Appliquees et Industrielles (SMAI)."

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 Modelisation et Statistique Spatiales published by Springer in the series Mathematiques & Applications, a series established by Societe de Mathematiques Appliquees et Industrielles (SMAI)."

La statistique spatiale connaA(R)t un dA(c)veloppement important du fait de son utilisation dans de nombreux domaines: sciences de la terre, environnement et climatologie, A(c)pidA(c)miologie, A(c)conomA(c)trie, analyse da (TM)image, etca ] Ce livre prA(c)sente les principaux modA]les spatiaux utilisA(c)s ainsi que leur statistique pour les trois types de donnA(c)es: gA(c)ostatistiques (observation sur un domaine continu), donnA(c)es sur rA(c)seau discret, donnA(c)es ponctuelles. La (TM)objectif est prA(c)senter de faAon concise mais mathA(c)matiquement complA]te les modA]les les plus classiques (second ordre et variogramme; modA]le latticiel et champ de Gibbs-Markov; processus ponctuels) ainsi que leur simulation par algorithme MCMC. Vient ensuite la prA(c)sentation des outils statistiques utiles A leur A(c)tude. De nombreux exemples utilisant R illustrent les sujets abordA(c)s. Chaque chapitre est complA(c)tA(c) par des exercices et une annexe prA(c)sente briA]vement les outils probabilistes et statistiques utiles A la statistique de champs alA(c)atoires.

In recent years spatial statistics has been widely applied in diverse areas such as climatology, ecology, economy, epidemiology, image analysis, etc. This volume illustrates the main spatial models and the current statistical methods for point-referenced, areal data and point pattern data with an emphasis on recent simulation techniques such as MCMC algorithms. The presentation is concise but mathematically rigorous and the proposed methods are illustrated using real data and the software R. Some exercises complete each chapter. The volume is accessible for senior undergraduate students, Ph.D. students in statistics, andexperienced statisticians. Moreover researchers in the above mentioned areas will find it useful as a mathematically sound reference.