Bayesian variable selection in non-homogeneous hidden Markov models through an evolutionary Monte Carlo method

Hidden Markov models (HMMs) are dynamic mixture models applied to time series in order to classify the observations into a small number of homogeneous groups, to understand when change points occur, and to model data heterogeneity through the switching between subseries with different state-dependent parameters. In the most general case, HMMs have an unobserved Markov chain whose transition probabilities are time-varying and dependent on exogenous variables through multinomial logit functions. When many covariates are available it is worthwhile selecting the subsets of variables which might affect most each row of the transition matrices. A Bayesian method for the stochastic selection of subsets of covariates is proposed by developing a novel evolutionary Monte Carlo algorithm. The methodology is illustrated and shown to be effective by performing experiments and comparisons on both synthetic data sets and a real multivariate time series with covariates.