Bayesian Nonparametric Mixture Modeling for Poisson Processes with an Application to Comparison of Single-Neuron Firing Intensities

• Activity Number: 457
• Type: Topic Contributed
• Date/Time: Wednesday, August 5, 2009 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Athanasios Kottas*+
• Companies: University of California, Santa Cruz
• Keywords: Beta mixtures ; Dirichlet process prior ; Neuronal data ; Scale uniform mixtures

Abstract

We present Bayesian nonparametric modeling for non-homogeneous Poisson processes (NHPPs) over time. The methodology exploits the connection of the NHPP intensity with a density function. Dirichlet process mixture models for this density yield flexible prior models for the NHPP, in particular, they enable, through appropriate choice of the mixture kernel, modeling for intensity functions with different types of shapes and smoothness properties. Simulation-based model fitting provides posterior inference for any functional of the NHPP that might be of interest. As an application, we consider comparison of the firing patterns of a neuron recorded under two distinct experimental conditions. We illustrate inferences for such comparison with two neurons recorded from the primary motor cortex area of a monkey's brain while performing a sequence of reaching tasks.