Statistical Inference for Spatial Processes

By: Brian D. Ripley

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Paperback | 16 September 1991

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160 Pages

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22.86 x 15.24 x 0.94

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The study of spatial processes and their applications is an important topic in statistics and finds wide application particularly in computer vision and image processing. This book is devoted to statistical inference in spatial statistics and is intended for specialists needing an introduction to the subject and to its applications. One of the themes of the book is the demonstration of how these techniques give new insights into classical procedures (including new examples in likelihood theory) and newer statistical paradigms such as Monte-Carlo inference and pseudo-likelihood. Professor Ripley also stresses the importance of edge effects and of lack of a unique asymptotic setting in spatial problems. Throughout, the author discusses the foundational issues posed and the difficulties, both computational and philosophical, which arise. The final chapters consider image restoration and segmentation methods and the averaging and summarising of images. Thus, the book will find wide appeal to researchers in computer vision, image processing, and those applying microscopy in biology, geology and materials science, as well as to statisticians interested in the foundations of their discipline.

Industry Reviews

' ... this monograph is required reading for anyone interested in the theory of spatial processes.' Biometrics 'All in all, a beautiful introduction to this important area and highly recommended.' Mededelingen van het Wiskundig Genootschap

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Preface	p. vii
Introduction	p. 1
Likelihood analysis for spatial Gaussian processes	p. 9
Spatial autoregressions	p. 11
Range parameters	p. 15
Discussion	p. 19
Edge corrections for spatial point processes	p. 22
Edge corrections for nearest neighbour methods	p. 24
Interpoint distance methods	p. 28
Asymptotic variances for edge-corrected estimates	p. 35
Limit theorems for interpoint distances	p. 44
Parameter estimation for Gibbsian point processes	p. 49
Definitions	p. 49
Local conditioning methods	p. 52
Approximate maximum likelihood	p. 55
Monte-Carlo approximations	p. 62
Discussion	p. 65
An example	p. 67
Modelling spatial images	p. 74
A general Bayesian approach	p. 76
Markov random field models	p. 79
Applications in astronomy	p. 82
Application to segmentation	p. 95
Other statistical approaches to segmentation	p. 113
Summarizing binary images	p. 121
Mathematical formulation	p. 123
A proposed summary	p. 128
Computation	p. 130
Examples	p. 131
Extensions	p. 135
References	p. 138
Index	p. 146
Table of Contents provided by Syndetics. All Rights Reserved.

Statistical Inference for Spatial Processes

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

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