Markov switching Dirichlet process mixture regression

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 nite mixture of conditionally independent Dirichlet process mixtures, with a Markov chain dening the mixing distribution. The proposed methodology focuses on settings where the number of subpopulations is small and can be assumed to be known, and exible 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 tting method for full posterior inference. Furthermore, we propose a general approach for inclusion of external covariates dependent on the Markov chain but condition-ally independent from the response. The methodology is applied to a problem from sheries research involving analysis of stock-recruitment data under shifts in the ecosystem state. © 2009 International Society for Bayesian Analysis.