Bayesian Analysis

Mixture Modeling for Marked Poisson Processes

Matthew A. Taddy and Athanasios Kottas

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We propose a general inference framework for marked Poisson processes observed over time or space. Our modeling approach exploits the connection of nonhomogeneous Poisson process intensity with a density function. Nonparametric Dirichlet process mixtures for this density, combined with nonparametric or semiparametric modeling for the mark distribution, yield flexible prior models for the marked Poisson process. In particular, we focus on fully nonparametric model formulations that build the mark density and intensity function from a joint nonparametric mixture, and provide guidelines for straightforward application of these techniques. A key feature of such models is that they can yield flexible inference about the conditional distribution for multivariate marks without requiring specification of a complicated dependence scheme. We address issues relating to choice of the Dirichlet process mixture kernels, and develop methods for prior specification and posterior simulation for full inference about functionals of the marked Poisson process. Moreover, we discuss a method for model checking that can be used to assess and compare goodness of fit of different model specifications under the proposed framework. The methodology is illustrated with simulated and real data sets.

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Bayesian Anal., Volume 7, Number 2 (2012), 335-362.

First available in Project Euclid: 16 June 2012

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Bayesian nonparametrics Beta mixtures Dirichlet process Marked point process Multivariate normal mixtures Non-homogeneous Poisson process Nonparametric regression


Taddy, Matthew A.; Kottas, Athanasios. Mixture Modeling for Marked Poisson Processes. Bayesian Anal. 7 (2012), no. 2, 335--362. doi:10.1214/12-BA711.

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