Nonparametric Bayesian Segmentation of a Multivariate Inhomogeneous Space-Time Poisson Process.

Journal Article (Journal Article)

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 are 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, Ohio, USA.

Full Text

Duke Authors

Cited Authors

  • Ding, M; He, L; Dunson, D; Carin, L

Published Date

  • December 2012

Published In

Volume / Issue

  • 7 / 4

Start / End Page

  • 813 - 840

PubMed ID

  • 23741284

Pubmed Central ID

  • PMC3670617

Electronic International Standard Serial Number (EISSN)

  • 1931-6690

International Standard Serial Number (ISSN)

  • 1936-0975

Digital Object Identifier (DOI)

  • 10.1214/12-ba727


  • eng