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Statistical Inference for Spatial Processes - B. D. Ripley

Statistical Inference for Spatial Processes

Paperback

Published: 16th September 1991
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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 to show 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 the 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 summarizing 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.

' ... 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

Prefacep. vii
Introductionp. 1
Likelihood analysis for spatial Gaussian processesp. 9
Spatial autoregressionsp. 11
Range parametersp. 15
Discussionp. 19
Edge corrections for spatial point processesp. 22
Edge corrections for nearest neighbour methodsp. 24
Interpoint distance methodsp. 28
Asymptotic variances for edge-corrected estimatesp. 35
Limit theorems for interpoint distancesp. 44
Parameter estimation for Gibbsian point processesp. 49
Definitionsp. 49
Local conditioning methodsp. 52
Approximate maximum likelihoodp. 55
Monte-Carlo approximationsp. 62
Discussionp. 65
An examplep. 67
Modelling spatial imagesp. 74
A general Bayesian approachp. 76
Markov random field modelsp. 79
Applications in astronomyp. 82
Application to segmentationp. 95
Other statistical approaches to segmentationp. 113
Summarizing binary imagesp. 121
Mathematical formulationp. 123
A proposed summaryp. 128
Computationp. 130
Examplesp. 131
Extensionsp. 135
Referencesp. 138
Indexp. 146
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521424202
ISBN-10: 0521424208
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 160
Published: 16th September 1991
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 22.66 x 15.22  x 0.91
Weight (kg): 0.25