Nonparametric Bayesian Segmentation of Multivariate Inhomogeneous Space-Time Poisson Process
Abstract
A nonparametric Bayesian model is proposed for segmenting time-evolving multivariate spatial point process data. An inhomogeneous Poisson process is assumed with a logistic stick-breaking process (LSBP) used to encourage piecewise-constant spatial Poisson intensities. The LSBP explicitly favors spatially contiguous segments and infers the number of segments based on the observed data. The temporal dynamics of the segmentation and of the Poisson intensities is modeled with exponential correlation in time, implemented in the form of a first-order autoregressive model for uniformly sampled discrete data, and via a Gaussian process with an exponential kernel for general temporal sampling. We consider and compare two different inference techniques: a Markov chain Monte Carlo sampler, which has relatively high computational complexity; and an approximate and efficient variational Bayesian analysis. The model is demonstrated with a simulated example and a real example of space-time crime events in Cincinnati, OH, USA.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 21, 2012
- Accession Number
- ADA577450
Entities
People
- David B. Dunson
- Lawrence Carin
- Lihan He
- Mingtao Ding
Organizations
- Duke University