Classification of Mixtures of Spatial Point Processes via Partial Bayes Factors

Motivated by the problem of minefield detection, we investigate the problem of classifying mixtures of spatial point processes. In particular we are interested in testing the hypothesis that a given dataset was generated by a Poisson process versus a mixture of a Poisson process and a hard-core Stra...

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Bibliographic Details
Published inJournal of computational and graphical statistics Vol. 14; no. 1; pp. 139 - 154
Main Authors Walsh, Daniel C.I, Raftery, Adrian E
Format Journal Article
LanguageEnglish
Published Alexandria Taylor & Francis 01.03.2005
American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America
Taylor & Francis Ltd
Subjects
Bayesian analysis
Datasets
Density estimation
Descriptive statistics
Edge effects
Hypotheses
Hypothesis testing
Minefield detection
Mining
Point estimators
Poisson process
Spatial models
Spatial points
Statistical analysis
Strauss process
Studies
Tessellations
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Summary:Motivated by the problem of minefield detection, we investigate the problem of classifying mixtures of spatial point processes. In particular we are interested in testing the hypothesis that a given dataset was generated by a Poisson process versus a mixture of a Poisson process and a hard-core Strauss process. We propose testing this hypothesis by comparing the evidence for each model by using partial Bayes factors. We use the term partial Bayes factor to describe a Bayes factor, a ratio of integrated likelihoods, based on only part of the available information, namely that information contained in a small number of functionals of the data. We applied our method to both real and simulated data, and considering the difficulty of classifying these point patterns by eye, our approach overall produced good results.
ISSN:1061-8600
1537-2715
DOI:10.1198/106186005X27149