AMS2005-2: A nonparametric Bayesian approach to inference for non-homogeneous Poisson processes

Athanasios Kottas
12/31/2005 09:00 AM
Applied Mathematics & Statistics
We propose modeling for Poisson processes over time, exploiting the connection of the Poisson process intensity with a density function. Nonparametric mixture models for this density induce flexible prior models for the intensity function.

We work with Beta densities for the mixture kernel and a Dirichlet process prior for the mixing distribution. We also discuss modeling for monotone intensity functions through scale uniform mixtures.

Simulation-based model fitting enables posterior inference for any feature of the Poisson process that might be of interest.

A data example illustrates the methodology.