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Biometrika 1975 62(2):467-475; doi:10.1093/biomet/62.2.467
© 1975 by Biometrika Trust
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A model for clustering

DAVID J. STRAUSS

Department of Statistics, University of California Riverside

A number of tests are available for the null hypothesis that a set of points in a region are scattered randomly, but relatively little is known about forms for the alternative. It is shown that under certain assumptions, the most severe of which is of Markov type, the probability density of the points must be of a simple explicit form depending on a single clustering parameter. The estimation of the parameter is studied and illustrated with an example.

Key Words: Clustering • Hammersley-Clifford theorem • Markov random field • Multidimensional point process • Persistence • Poisson process


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