  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.
