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Information criteria for inhomogeneous spatial point processes

By Achmad Choiruddin, Jean-François Coeurjolly and Rasmus Waagepetersen
CSGB Research Reports
No. 04, March 2020

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.

Keywords: Akaike's information criterion, Bayesian information criterion, composite information criterion, composite likelihood, inhomogeneous point process, intensity function, model selection.

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