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We propose a sparse vector autoregressive (VAR) hidden semi-Markov model(HSMM) for modeling temporal and contemporaneous (e.g. spatial) dependencies inmultivariate nonstationary time series. The HSMM's generic state distributionis embedded in a special transition matrix structure, facilitating efficientlikelihood evaluations and arbitrary approximation accuracy. To promotesparsity of the VAR coefficients, we deploy an $l_1$-ball projection prior,which combines differentiability with a positive probability of obtaining exactzeros, achieving variable selection within each switching state. This alsofacilitates posterior estimation via Hamiltonian Monte Carlo (HMC). We furtherplace non-local priors on the parameters of the HSMM dwell distributionimproving the ability of Bayesian model selection to distinguish whether thedata is better supported by the simpler hidden Markov model (HMM), or the moreflexible HSMM. Our proposed methodology is illustrated via an application tohuman gesture phase segmentation based on sensor data, where we successfullyidentify and characterize the periods of rest and active gesturing, as well asthe dynamical patterns involved in the gesture movements associated with eachof these states.

Bayesian Sparse Vector Autoregressive Switching Models with Application to Human Gesture Phase Segmentation