UCSC-SOE-20-07: Erlang mixture modeling for Poisson process intensities

Hyotae Kim and Athanasios Kottas
09/01/2020 10:51 AM
We develop a prior probability model for temporal Poisson process intensities through structured mixtures of Erlang densities with common scale parameter, mixing on the integer shape parameters. The mixture weights are constructed through increments of a cumulative intensity function which is modeled nonparametrically with a gamma process prior. Such model specification provides a novel extension of Erlang mixtures for density estimation to the intensity estimation setting. The prior model structure supports general, non-standard shapes for the point process intensity function, and it also enables effective handling of the Poisson process likelihood normalizing constant resulting in efficient posterior simulation. The Erlang mixture modeling approach is further elaborated to obtain inference for spatial Poisson processes. The methodology is illustrated with synthetic and real data examples.