Mixture Modeling for Marked Poisson Processes

By Matt Taddy, Athanasios Kottas. 2010

71 citations recorded by the source corpus.

We propose a general modeling framework for marked Poisson processes observed over time or space. The modeling approach exploits the connection of the 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.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/36da734570ffbfcb3899e0c4763a8fdc9be9422a

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Citations in the corpus

Reactive point processes: A new approach to predicting power failures in underground electrical systems (2015, methodology): “Being able to predict manhole events accurately in the short term could immediately lead to reduced risks to public safety and increased reliability of electrical service.”
Bayesian Nonparametric Modeling for Multivariate Ordinal Regression (2014, background): “…proposed by Müller, Erkanli, and West (1996) in the context of continuous variables, and has been more recently studied under different modeling scenarios; see, for example, Müller and Quintana (2010), Park and Dunson (2010), Taddy and Kottas (2010), Taddy and Kottas (2012), and Wade et al. (2014).”
Bayesian Inference and Model Assessment for Spatial Point Patterns Using Posterior Predictive Samples (2017, background): “See, e.g., Kottas and Sansó (2007) and Taddy and Kottas (2012).”