Infinite Hidden Markov Model for Multiple Multivariate Time Series with Missing Data

• Activity Number: 348 - ENVR Student Paper Award Winners
• Type: Topic-Contributed
• Date/Time: Thursday, August 12, 2021 : 10:00 AM to 11:50 AM
• Sponsor: Section on Statistics and the Environment
• Author(s): Lauren Hoskovec* and Kirsten Koehler and Jennifer L. Peel and John Volckens and Matthew David Koslovsky and Ander Wilson
• Companies: Colorado State University and Johns Hopkins University and Colorado State University and Colorado State University and Colorado State University and Colorado State University
• Keywords: multivariate time series; time-resolved exposures; missing data; multiple imputation; Bayesian inference

Abstract

Recent technological advancements permit the collection of time-resolved personal exposure data for a sample of people. Such data is often incomplete with missing observations and exposures below the limit of detection. In this paper we develop an infinite hidden Markov model for multiple multivariate time series with missing data. Our model is designed to flexibly include covariates to inform the allocation of time points to 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 for missing data. In simulation studies, our model excels in estimating hidden states and state-specific parameters on data sets with varying levels of missing data. We validate our imputation approach on real data and demonstrate our model's robustness to covariate structure. In a data analysis, we demonstrate the inferential gains obtained from our model including imputation, hidden states that characterize exposure more fully than manually assigned microenvironments, and identification of both shared and unique hidden state trajectories among repeated sampling days for the same person.