Bayesian adaptive group lasso with semiparametric hidden Markov models.

This paper presents a Bayesian adaptive group least absolute shrinkage and selection operator method to conduct simultaneous model selection and estimation under semiparametric hidden Markov models. We specify the conditional regression model and the transition probability model in the hidden Markov model into additive nonparametric functions of covariates. A basis expansion is adopted to approximate the nonparametric functions. We introduce multivariate conditional Laplace priors to impose adaptive penalties on regression coefficients and different groups of basis expansions under the Bayesian framework. An efficient Markov chain Monte Carlo algorithm is then proposed to identify the nonexistent, constant, linear, and nonlinear forms of covariate effects in both conditional and transition models. The empirical performance of the proposed methodology is evaluated via simulation studies. We apply the proposed model to analyze a real data set that was collected from the Alzheimer's Disease Neuroimaging Initiative study. The analysis identifies important risk factors on cognitive decline and the transition from cognitive normal to Alzheimer's disease.