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

TL;DR

This paper introduces a Bayesian HSMM that incorporates covariate-dependent state durations and a data subsampling method to analyze high-frequency environmental data, improving modeling of state durations influenced by external factors.

Contribution

The authors extend traditional HSMMs by allowing state duration parameters to vary with covariates and propose a subsampling approach for high-frequency data, enhancing model flexibility and applicability.

Findings

Identified significant covariate effects on state durations in lake data.

Demonstrated improved modeling of environmental state changes.

Provided insights into blue-green algae dynamics.

Abstract

Environmental time series data observed at high frequencies can be studied with 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 a discrete-time HSMM, the duration in each state can be modeled with a zero-truncated Poisson distribution, where the duration parameter may be state-specific but constant in time. We extend the HSMM by allowing the state-specific duration parameters to vary in time and model them as a function of known covariates observed over a period of time leading up to a state transition. In addition, we propose a data subsampling approach given that high-frequency data can violate the conditional independence assumption of the HSMM. We apply the model to high-frequency data collected by an instrumented buoy in Lake Mendota. We model the phycocyanin concentration, which is used in aquatic systems to estimate the relative abundance of blue-green algae, and identify important time-varying effects associated with the duration in each state.