Spatial Statistics and Modeling

ISBN-13: 9781461424994 / Angielski / Miękka / 2012 / 302 str.

Carlo Gaetan; Xavier Guyon

Opis

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).

Recenzje

From the reviews:

"Spatial statistics aims to develop models and statistical inference methods for observations that have a distinct spatial location component. ... The book under review presents theory simulation and statistical applications in a well-structured manner and even covers some modern topics from the very recent journal literature. ... To summarise this book is a welcome addition to the literature on spatial statistics and is perfectly suitable for designing a lecture course in this area." (Ilya S. Molchanov, Mathematical Reviews, Issue 2011 a)

"Students and researchers in statistics, geology, image processing, spatial economics, earth sciences, epidemiology, and other areas. ... authors of the current book do an excellent job in selecting ... the most relevant topics for a new investigator just venturing into this exciting area. ... well structured, accessible, and easy to read without compromising the theoretical rigor of the subject. ... Any researcher interested in statistical methodologies for brain imaging will find the book quite engaging. This book will have a permanent place in my bookshelf." (Rajesh Ranjan Nandy, International Statistical Review, Vol. 78 (3), 2010)

"This book is the English translation of Modélisation et Statistique Spatiales, published by Springer in the series Mathématiques & Applications ... . it is intended as a text for a graduate level course." (Donald E. Myers, Mathematical Geosciences, Vol. 42, July, 2010)

Spis treści

Second-order spatial models and geostatistics.- Gibbs-Markov random fields on networks.- Spatial point processes.- Simulation of spatial models.- Statistics for spatial models.

Blurb

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).

Carlo Gaetan is Associate Professor of Statistics in the Department of Statistics at the Ca' Foscari University of Venice.

Xavier Guyon is Professor  Emeritus at the University of Paris 1 Panthéon-Sorbonne. He is author of a Springer monograph on random fields.