Infinite hidden Markov models for multiple multivariate time series with missing data

Lauren Hoskovec, Matthew D. Koslovsky, Kirsten Koehler, Nicholas Good, Jennifer L. Peel, John Volckens, Ander Wilson

Research output: Contribution to journalArticlepeer-review


Exposure to air pollution is associated with increased morbidity and mortality. Recent technological advancements permit the collection of time-resolved personal exposure data. Such data are often incomplete with missing observations and exposures below the limit of detection, which limit their use in health effects studies. In this paper, we develop an infinite hidden Markov model for multiple asynchronous multivariate time series with missing data. Our model is designed to include covariates that can inform transitions among hidden states. We implement beam sampling, a combination of slice sampling and dynamic programming, to sample the hidden states, and a Bayesian multiple imputation algorithm to impute missing data. In simulation studies, our model excels in estimating hidden states and state-specific means and imputing observations that are missing at random or below the limit of detection. We validate our imputation approach on data from the Fort Collins Commuter Study. We show that the estimated hidden states improve imputations for data that are missing at random compared to existing approaches. In a case study of the Fort Collins Commuter Study, we describe the inferential gains obtained from our model including improved imputation of missing data and the ability to identify shared patterns in activity and exposure among repeated sampling days for individuals and among distinct individuals.

Original languageEnglish (US)
Pages (from-to)2592-2604
Number of pages13
Issue number3
StatePublished - Sep 2023
Externally publishedYes


  • Bayesian inference
  • hidden Markov models
  • multiple imputation
  • multiple time series

ASJC Scopus subject areas

  • General Immunology and Microbiology
  • Applied Mathematics
  • General Biochemistry, Genetics and Molecular Biology
  • General Agricultural and Biological Sciences
  • Statistics and Probability


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