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December 2009 Markov switching Dirichlet process mixture regression
Athanasios Kottas, Matthew A. Taddy
Bayesian Anal. 4(4): 793-816 (December 2009). DOI: 10.1214/09-BA430

Abstract

Markov switching models can be used to study heterogeneous populations that are observed over time. This paper explores modeling the group characteristics nonparametrically, under both homogeneous and nonhomogeneous Markov switching for group probabilities. The model formulation involves a finite mixture of conditionally independent Dirichlet process mixtures, with a Markov chain defining the mixing distribution. The proposed methodology focuses on settings where the number of subpopulations is small and can be assumed to be known, and flexible modeling is required for group regressions. We develop Dirichlet process mixture prior probability models for the joint distribution of individual group responses and covariates. The implied conditional distribution of the response given the covariates is then used for inference. The modeling framework allows for both non-linearities in the resulting regression functions and non-standard shapes in the response distributions. We design a simulation-based model fitting method for full posterior inference. Furthermore, we propose a general approach for inclusion of external covariates dependent on the Markov chain but conditionally independent from the response. The methodology is applied to a problem from fisheries research involving analysis of stock-recruitment data under shifts in the ecosystem state.

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Athanasios Kottas. Matthew A. Taddy. "Markov switching Dirichlet process mixture regression." Bayesian Anal. 4 (4) 793 - 816, December 2009. https://doi.org/10.1214/09-BA430

Information

Published: December 2009
First available in Project Euclid: 22 June 2012

zbMATH: 1330.62141
MathSciNet: MR2570089
Digital Object Identifier: 10.1214/09-BA430

Rights: Copyright © 2009 International Society for Bayesian Analysis

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Vol.4 • No. 4 • December 2009
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