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Environmental time series data observed at high frequencies can be studiedwith approaches such as hidden Markov and semi-Markov models (HMM and HSMM).HSMMs extend the HMM by explicitly modeling the time spent in each state. In adiscrete-time HSMM, the duration in each state can be modeled with azero-truncated Poisson distribution, where the duration parameter may bestate-specific but constant in time. We extend the HSMM by allowing thestate-specific duration parameters to vary in time and model them as a functionof known covariates observed over a period of time leading up to a statetransition. In addition, we propose a data subsampling approach given thathigh-frequency data can violate the conditional independence assumption of theHSMM. We apply the model to high-frequency data collected by an instrumentedbuoy in Lake Mendota. We model the phycocyanin concentration, which is used inaquatic systems to estimate the relative abundance of blue-green algae, andidentify important time-varying effects associated with the duration in eachstate.

A Bayesian Hidden Semi-Markov Model with Covariate-Dependent State Duration Parameters for High-Frequency Environmental Data