Bayesian variable selection in Markov mixture models

Bayesian methods for variable selection and model choice have become increasingly popular in recent years, due to advances in Markov Chain Monte Carlo (MCMC) computational algorithms. Several methods have been proposed in literature in the case of linear and generalized linear models. In this article, we adapt some of the most popular algorithms to a class of nonlinear and non Gaussian time series models, i.e., the Markov Mixture Models (MMM). We also propose the "Metropolization" of the algorithm of Kuo and Mallick (1998), in order to tackle variable selection efficiently, both when the complexity of the model is high, as in MMM, and when the exogenous variables are strongly correlated. Numerical comparisons among the competing MCMC algorithms are also presented via simulation examples.