空间统计学理论——概述(英文)

本书是一部统计学方面的专著，每章首先介绍理论，其次使用资源R包将其应用于说明性示例中，列出一些练习，最后以参考文献结尾。本书共分为4章，介绍了网格数据点、单位面积数据点、映射点模式数据、高斯随机域、平稳性概念、协方差函数的构造、简单克里格方法、半方差函数、贝叶斯估计、离散随机域、高斯自回归模型、马尔可夫随机域、欧几里得空间上的点过程、泊松过程、有限点过程、分层建模等内容。本书适合数学、工程学、统计学研究生参考阅读。

Preface

Author

CHAPTER 1 Introduction

1.1 GRIDDED DATA

1.2 AREAL UNIT DATA

1.3 MAPPED POINT PATTERN DATA

1.4 PLAN OF THE BOOK

CHAPTER 2 Random field modelling and interpolation

2.1 RANDOM FIELDS

2.2 GAUSSIAN RANDOM FIELDS

2.3 STATIONARITY CONCEPTS

2.4 CONSTRUCTION OF COVARIANCE FUNCTIONS

2.5 PROOF OF BOCHNER'S THEOREM

2.6 THE SEMI-VARIOGRAM

2.7 SIMPLEKRIGING

2.8 BAYES ESTIMATOR

2.9 ORDINARY KRIGING

2.10 UNIVERSAL KRIGING

2.11 WORKED EXAMPLES WITH R

2.12 EXERCISES

2.13 POINTERS TO THE LITERATURE

CHAPTER 3 Models and inference for areal unit data

3.1 DISCRETE RANDOM FIELDS etnefno

3.2 GAUSSIAN AUTOREGRESSION MODELS

3.3 GIBBS STATES

3.4 MARKOV RANDOM FIELDS

3.5 INFERENCE FOR AREAL UNIT MODELS

3.6 MARKOV CHAIN MONTE CARLO SIMULATION

3.7 HIERARCHICAL MODELLING

3.7.1 Image segmentation

3.7.2 Disease mapping

3.7.3 Synthesis

3.8 WORKED EXAMPLES WITH R

3.9 EXERCISES

3.10 POINTERS TO THE LITERATURE

CHAPTER 4 Spatial point processes

4.1 POINT PROCESSES ON EUCLIDEAN SPACES

4.2 THE POISSON PROCESS

4.3 MOMENT MEASURES

4.4 STATIONARITY CONCEPTS AND PRODUCT DENSITIES

4.5 FINITE POINT PROCESSES

4.6 THE PAPANGELOU CONDITIONAL INTENSITY

4.7 MARKOV POINT PROCESSES

4.8 LIKELIHOOD INFERENCE FOR POISSON PROCESSES

4.9 INFERENCE FOR FINITE POINT PROCESSES

4.10 COX PROCESSES

4.10.1 Cluster processes

4.10.2 Log-Gaussian Cox processes

4.10.3 Minimum contrast estimation

4.11 HIERARCHICAL MODELLING

4.12 WORKED EXAMPLES WITH R

4.13 EXERCISES

4.14 POINTERS TO THE LITERATURE

Appendix：Solutions to theoretical exercises

Index

编辑手记