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Information criteria for inhomogeneous spatial point processes
Author(s) -
Choiruddin Achmad,
Coeurjolly JeanFrançois,
Waagepetersen Rasmus
Publication year - 2021
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/anzs.12327
Subject(s) - akaike information criterion , bayesian information criterion , mathematics , point process , information criteria , poisson distribution , context (archaeology) , bayesian probability , model selection , deviance information criterion , point (geometry) , cox process , bayesian inference , statistics , mathematical optimization , poisson process , paleontology , geometry , biology
Summary The theoretical foundation for a number of model selection criteria is established in the context of inhomogeneous point processes and under various asymptotic settings: infill, increasing domain and combinations of these. For inhomogeneous Poisson processes we consider Akaike's information criterion and the Bayesian information criterion, and in particular we identify the point process analogue of ‘sample size’ needed for the Bayesian information criterion. Considering general inhomogeneous point processes we derive new composite likelihood and composite Bayesian information criteria for selecting a regression model for the intensity function. The proposed model selection criteria are evaluated using simulations of Poisson processes and cluster point processes.