Bayesian Inference for Nonhomogeneous Hidden Semi-Markov Models

This paper proposes a novel Bayesian framework for the estimation of nonhomogeneous hidden semi-Markov models, where the underlying state dynamic is governed by time-varying covariates and sojourn times. Our methodology employs a Markov Chain Monte Carlo inference procedure that naturally accommodates the hierarchical structure of latent-state models, avoiding both approximations and computational burden induced by augmented-state formulations, typically required in sequential data methods. The proposal is first validated on simulated data and subsequently applied to a benchmark dataset. Particularly, the case study focuses on a bivariate time series of wind and wave directions recorded by the Ancona buoy in the Adriatic Sea, with wind speed included as a time-varying exogenous covariate.