Abstract
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.
Original language | English |
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Journal | Australian and New Zealand Journal of Statistics |
Volume | 63 |
Issue number | 1 |
Pages (from-to) | 119-143 |
Number of pages | 25 |
ISSN | 1369-1473 |
DOIs | |
Publication status | Published - Mar 2021 |
Bibliographical note
Funding Information:The research of J.-F. Coeurjolly is supported by the Natural Sciences and Engineering Research Council. Rasmus Waagepetersen is supported by The Danish Council for Independent Research ? Natural Sciences, grant DFF - 7014-00074 ?Statistics for point processes in space and beyond?, and by the Centre for Stochastic Geometry and Advanced Bioimaging, funded by grant 8721 from the Villum Foundation.
Publisher Copyright:
© 2021 John Wiley & Sons Australia, Ltd
Keywords
- Akaike's information criterion
- Bayesian information criterion
- composite information criterion
- composite likelihood
- inhomogeneous point process
- intensity function
- model selection