tBayes-MICE: A Bayesian Approach to Multiple Imputation for Time Series Data

TL;DR

tBayes-MICE introduces a Bayesian extension to the MICE method for time series data, improving imputation accuracy and uncertainty quantification using MCMC sampling.

Contribution

It extends MICE with Bayesian inference, incorporating time-aware features and evaluating performance with real datasets and advanced samplers.

Findings

tBayes-MICE reduces imputation errors across variables.

MALA sampler provides more consistent posterior exploration.

The method balances accuracy with uncertainty quantification.

Abstract

Time-series analysis is often affected by missing data, a common problem across several fields, including healthcare and environmental monitoring. Multiple Imputation by Chained Equations (MICE) has been prominent for imputing missing values through "fully conditional specification". We extend MICE using the Bayesian framework (tBayes-MICE), utilising Bayesian inference to impute missing values via Markov Chain Monte Carlo (MCMC) sampling to account for uncertainty in MICE model parameters and imputed values. We also include temporally informed initialisation and time-lagged features in the model to respect the sequential nature of time-series data. We evaluate the tBayes-MICE method using two real-world datasets (AirQuality and PhysioNet), and using both the Random Walk Metropolis (RWM) and the Metropolis-Adjusted Langevin Algorithm (MALA) samplers. Our results demonstrate that tBayes-MICE reduces imputation errors relative to the baseline methods over all variables and accounts for uncertainty in the imputation process, thereby providing a more accurate measure of imputation error. We also found that MALA mixed better than RWM across most variables, achieving comparable accuracy while providing more consistent posterior exploration. Overall, these findings suggest that the tBayes-MICE framework represents a practical and efficient approach to time-series imputation, balancing increased accuracy with meaningful quantification of uncertainty in various environmental and clinical settings.