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

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 exible 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 tting enables posterior inference for any feature of the Poisson process that might be of interest. A data example illustrates the methodology