Hierarchical Bayesian modeling of marked non-homogeneous Poisson processes with finite mixtures and inclusion of covariate information

Abstract

We investigate marked non-homogeneous Poisson processes using finite mixtures of bivariate normal components to model the spatial intensity function. We employ a Bayesian hierarchical framework for estimation of the parameters in the model, and propose an approach for including covariate information in this context. The methodology is exemplified through an application involving modeling of and inference for tornado occurrences.

Keywords:

• birth–death Markov chain Monte Carlo
• data augmentation
• marked point processes
• mixture models
• non-homogeneous Poisson process

Acknowledgements

This research was supported by NSF DMS-1007478 grant. The author is grateful to Professors Noel Cressie and David Matteson, for helpful comments regarding an earlier version of the manuscript, and to two referees for their constructive suggestions.