Bayesian Analysis

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

Mingtao Ding, Lihan He, David Dunson, and Lawrence Carin

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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 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.

Article information

Source
Bayesian Anal., Volume 7, Number 4 (2012), 813-840.

Dates
First available in Project Euclid: 27 November 2012

Permanent link to this document
https://projecteuclid.org/euclid.ba/1354024463

Digital Object Identifier
doi:10.1214/12-BA727

Mathematical Reviews number (MathSciNet)
MR3000015

Zentralblatt MATH identifier
1330.62353

Keywords
Bayesian hierarchical model spatial segmentation temporal dynamics Gaussian process logistic stick breaking process inhomogeneous Poisson process

Citation

Ding, Mingtao; He, Lihan; Dunson, David; Carin, Lawrence. Nonparametric Bayesian Segmentation of a Multivariate Inhomogeneous Space-Time Poisson Process. Bayesian Anal. 7 (2012), no. 4, 813--840. doi:10.1214/12-BA727. https://projecteuclid.org/euclid.ba/1354024463


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