Athanasios Kottas (UC Santa Cruz)
Nonparametric mixture modeling for Poisson processes
We present Bayesian nonparametric modeling for non-homogeneous Poisson processes over time or
space. The methodology exploits the connection of the Poisson process intensity with a density function.
Dirichlet process mixture models for the point process density yield flexible prior models for the Poisson
process. In particular, through appropriate choice of the mixture kernel, the modeling framework enables
different shapes and properties for the intensity function depending on the context and application.
Simulation-based model fitting provides posterior inference for any functional of the Poisson process that
might be of interest. The modeling approach will be illustrated with applications in neuronal data
analysis, involving comparison of the firing patterns of a neuron recorded under two distinct experimental
conditions, as well as extreme value analysis, involving estimation of intensity of extremes over time. An
extension to modeling for marked Poisson processes will also be discussed. Here, the model formulation
builds the mark density and intensity function from a joint nonparametric mixture. A key feature of such
models is that they yield general specifications for the corresponding conditional mark distribution
resulting in flexible inference for different types of marks.