空间统计与建模

空间统计在气候学、生态学、经济学、环境和地球科学、流行病学、图像分析等多种学科中都很有用。这本书涵盖了三类空间数据最著名的空间模型：地质统计数据（平稳性、内在模型、变异函数、空间回归和时空模型）、区域数据（吉布斯-马尔可夫场和空间自回归）和点模式数据（泊松、考克斯、吉布斯和马尔可夫点过程）。水平相对较高，陈述简洁而完整。
描述了最重要的统计方法及其渐近性质，包括地质统计学中的估计、自相关和二阶统计、最大似然方法、使用伪似然或蒙特卡罗模拟的近似推断、点过程的统计和贝叶斯层次模型。一章专门介绍马尔可夫链蒙特卡罗模拟（吉布斯采样器、大都会黑斯廷斯算法和精确模拟）。
大量的实例都是用R研究的，每一章最后都有一套理论和应用练习。虽然假设有概率和数理统计的基础，但三个附录介绍了一些必要的背景。这本书适合具有扎实数学背景的高年级本科生和统计学博士生阅读。此外，在上述领域经验丰富的统计学家和研究人员会发现这本书作为一个数学上合理的参考书很有价值。
这本书是斯普林格在《数学与应用》系列中出版的《现代与统计空间》的英文译本，该系列由法国数学与工业协会（SMAI）建立。
卡洛·盖坦（Carlo Gaetan）是威尼斯卡福斯卡里大学统计系的统计学副教授。
Xavier Guyon是巴黎大学索邦分校的名誉教授。他是关于随机场的斯普林格专著的作者。
Spatial Statistics and Modeling
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.

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