Modeling state duration and emission dependence in hidden Markov and hidden semi-Markov models

Abstract

Hidden Markov models (HMM) are composed of a latent state sequence and an observation sequence conditionally independent on the states, which follows an emission distribution. Hidden semi-Markov models (HSMM) extend the HMM by explicitly modeling the duration in the states. This dissertation expands the HSMM by introducing non-homogeneity in the duration model, with duration parameters defined as functions of time-varying covariates, which has not been considered to date. This model is applied to high-frequency environmental data. The variable transition HMM (VTHMM) also expands the HMM by considering the duration in the state transition probabilities. We present a VTHMM for team sports data to obtain inference on the dynamic network of players in a game, and model high temporal resolution player location data. Lastly, the conditional independence assumption in the emission distribution can be violated, in particular with high-frequency data. We propose two novel approaches to address the conditional dependence, by introducing data subsampling in the MCMC sampling algorithm for parameter inference in HMMs and HSMMs, and by considering basis function expansions in the emission distribution.