Computational methods for multiplicative intensity models using weighted gamma processes: Proportional hazards, marked point processes, and panel count data

We develop computational procedures for a class of Bayesian nonparametric and semiparametric multiplicative intensity models incorporating kernel mixtures of spatial weighted gamma measures. A key feature of our approach is that explicit expressions for posterior distributions of these models share many common structural features with the posterior distributions of Bayesian hierarchical models using the Dirichlet process. Using this fact, along with an approximation for the weighted gamma process, we show that with some care, one can adapt efficient algorithms used for the Dirichlet process to this setting. We discuss blocked Gibbs sampling procedures and Polya urn Gibbs samplers. We illustrate our methods with applications to proportional hazard models, Poisson spatial regression models, recurrent events, and panel count data.