Functional concurrent hidden Markov model

This study considers a functional concurrent hidden Markov model. The proposed model consists of two components. One is a transition model for elucidating how potential covariates influence the transition probability from one state to another. The other is a conditional functional linear concurrent regression model for characterizing the state-specific effects of functional covariates. A distribution-free random effect is introduced to the conditional model to describe the dependency of individual functional observations. The soft-thresholding operator and the adaptive group lasso are introduced to simultaneously accommodate the local and global sparsity of the functional coefficients. A Bayesian approach is developed to jointly conduct estimation, variable selection, and the detection of zero-effect regions. This proposed approach incorporates the dependent Dirichlet process with stick-breaking prior for accommodating the unspecified distribution of the random effect and a blocked Gibbs sampler for efficient posterior sampling. Finally, the empirical performance of the proposed method is evaluated through simulation studies, and the utility of the methodology is demonstrated by an application to the analysis of air pollution and meteorological data.