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Spatial statistics and computational methods空间统计学与计算方法

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作者：Jesper MÃ¸ller　著著

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出版时间：2003-3-1

I S B N：9780387001364

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Spatial statistics and computational methods空间统计学与计算方法

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Spatial statistics and computational methods空间统计学与计算方法

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内容简介

Spatial statistics and Markov Chain Monte Carlo (MCMC) techniques have each undergone major developments in the last decade. Also, these two areas are mutually reinforcing, because MCMC methods are often necessary for the practical implementation of spatial statistical inference, while new spatial stochastic models in turn motivate the development of improved MCMC algorithms. This volume shows how sophisticated spatial statistical and computational methods apply to a range of problems of increasing importance for applications in science and technology. It consists of four chapters: 1. Petros Dellaportas and Gareth O. Roberts give a tutorial on MCMC methods, the computational methodology which is essential for virtually all the complex spatial models to be considered in subsequent chapters. 2. Peter J. Diggle, Paulo J, Ribeiro Jr., and Ole F. Christensen introduce the reader to the model-based approach to geostatistics, i.e. the application of general statistical principles to the formulation of explicit stochastic models for geostatistical data, and to inference within a declared class of models. 3. Merrilee A. Hurn, Oddvar K. Husby, and Håvard Rue discuss various aspects of image analysis, ranging from low to high level tasks, and illustrated with different examples of applications. 4. Jesper Moller and Rasmus P. Waggepetersen collect recent theoretical advances in simulation-based inference for spatial point processes, and discuss some examples of applications. The volume introduces topics of current interest in spatial and computational statistics, which should be accessible to postgraduate students as well as to experienced statistical researchers. It is partly based on the course material for the "TMR and MaPhySto Summer School on Spatial Statistics and Computational Methods," held at Aalborg University, Denmark, August 19-22, 2001. The editor, Jesper Moller, Professor of statistics at Aalborg University, and the above-mentioned contributors have all been associated with the European Union's TMR network "Statistics and Computational Methods for the Analysis of Spatial Data. ERB-FMRX-CT96-0095."

作者简介

Preface
Contributors
1 An Introduction to MCMC
　1.1 MCMC and spatial statistics
　1.2 The Gibbs sampler
　1.3 The Metropolis-Hastings algorithm
　1.4 MCMC Theory
　1.5 Practical implementation
　1.6 An illustrative example
　1.7 Appendix: Model determination using MCMC
2 An Introduction to Model-Based Geostatistics
　2.1 Introduction
　2.2 Examples of geostatistical problems
　2.3 The general geostatistical model
　2.4 The Gaussian Model
　2.5 Parametric estimation of covariance structure
　2.6 Plug-in prediction
　2.7 Bayesian inference for the linear Gaussian model
　2.8 A Case Study: the Swiss rainfall data
　2.9 Generalised linear spatial models
　2.10 Discussion
　2.11 Software
　2.12 Further reading
3 A Tutorial on Image Analysis
　3.1 Introduction
　3.2 Markov random field models
　3.3 Models for binary and categorical images
　3.4 Image estimators and the treatment of parameters
　3.5 Grey-level images
　3.6 High-level imaging
　3.7 An example in ultrasound imaging
4 An Introduction to Simulation-Based Inference for Spatial Point Processes
　4.1 Introduction
　4.2 Illustrating examples
　4.3 What is a spatial point process?
　4.4 Poisson point processes
　4.5 Summary statistics
　4.6 Models and simulation-based inference for aggregated point patterns
　4.7 Models and simulation-based inference for Markov point processes
　4.8 Further reading and concluding remarks
Index