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On Bayesian Inference for the K Function
Author(s) -
Bognar Matthew A.
Publication year - 2006
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.200410166
Subject(s) - inference , bayesian probability , bayesian inference , mathematics , statistical inference , frequentist inference , function (biology) , statistics , econometrics , computer science , artificial intelligence , biology , evolutionary biology
The K function is a summary of spatial dependence in spatial point processes. In practice one observes a realization of the spatial point process, called a spatial point pattern. Although the K function of a spatial point process is typically unknown, several estimators of the process K function have been put forth. These estimators, however, are based upon empirical averages; the complicated distributional properties of the estimators unfortunately complicates interval estimation. In this paper, we propose a Bayesian inferential framework, allowing inference for the K function of the spatial point process (including interval estimation). Of particular interest is the unique use of the posterior predictive distribution to (efficiently) enable such inferences. To demonstrate our technique, the well known Swedish pine sapling data (Strand, 1972) is analyzed, including a discussion on evaluating model fit. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)