Bayesian Analysis

A Bayesian Nonparametric Spiked Process Prior for Dynamic Model Selection

Alberto Cassese, Weixuan Zhu, Michele Guindani, and Marina Vannucci

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In many applications, investigators monitor processes that vary in space and time, with the goal of identifying temporally persistent and spatially localized departures from a baseline or “normal” behavior. In this manuscript, we consider the monitoring of pneumonia and influenza (P&I) mortality, to detect influenza outbreaks in the continental United States, and propose a Bayesian nonparametric model selection approach to take into account the spatio-temporal dependence of outbreaks. More specifically, we introduce a zero-inflated conditionally identically distributed species sampling prior which allows borrowing information across time and to assign data to clusters associated to either a null or an alternate process. Spatial dependences are accounted for by means of a Markov random field prior, which allows to inform the selection based on inferences conducted at nearby locations. We show how the proposed modeling framework performs in an application to the P&I mortality data and in a simulation study, and compare with common threshold methods for detecting outbreaks over time, with more recent Markov switching based models, and with spike-and-slab Bayesian nonparametric priors that do not take into account spatio-temporal dependence.

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Bayesian Anal., Volume 14, Number 2 (2019), 553-572.

First available in Project Euclid: 10 August 2018

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nonparametric Bayes variable selection Markov random field spatio-temporal data

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Cassese, Alberto; Zhu, Weixuan; Guindani, Michele; Vannucci, Marina. A Bayesian Nonparametric Spiked Process Prior for Dynamic Model Selection. Bayesian Anal. 14 (2019), no. 2, 553--572. doi:10.1214/18-BA1116.

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