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Mathematics - Probability Theory and Stochastic Processes | Spatial Statistics and Modeling

Spatial Statistics and Modeling

Gaetan, Carlo, Guyon, Xavier

2010

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  • Clear and precise presentation of the most important spatial models, including their probabilistic properties and related statistical methods
  • Implements these models and studies their statistics on a wide variety of real spatial data coming from real-world applications
  • Each chapter has numerous exercises to test the reader, and R scripts are provided (see the book’s web page) to help students and researchers deepen their understanding of the subject

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.

Content Level » Research

Keywords » Applied statistics - Geostatistics - Markov random field - Point process - Spatial statistics and modeling - algorithms - mathematical statistics

Related subjects » Earth Sciences & Geography - Econometrics / Statistics - Probability Theory and Stochastic Processes - Statistical Theory and Methods

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