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

2026-03-28

AI Summary

This study addresses the critical challenge of missing values in time series, which severely compromise analytical accuracy in domains such as healthcare and environmental monitoring. The authors propose a novel imputation method that integrates Bayesian inference with Multiple Imputation by Chained Equations (MICE), marking the first incorporation of a Bayesian framework into MICE for time series data. By jointly modeling the uncertainty of both model parameters and imputed values through time-lagged features, time-aware initialization, and Markov Chain Monte Carlo (MCMC) sampling—specifically Random Walk Metropolis (RWM) and Metropolis-Adjusted Langevin Algorithm (MALA)—the approach embeds temporal structural constraints to enhance imputation plausibility. Experiments on AirQuality and PhysioNet datasets demonstrate substantially reduced imputation errors, with MALA exhibiting faster convergence and more stable posterior exploration than RWM, yielding higher accuracy and reliable 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 (Bayes-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 Bayes-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 Bayes-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 converges faster than RWM, achieving comparable accuracy while providing more consistent posterior exploration. Overall, these findings suggest that the Bayes-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.

Problem

• missing data
• time series
• multiple imputation
• Bayesian inference
• uncertainty quantification

Innovation

• Bayesian inference
• Multiple Imputation
• Time Series
• MCMC sampling
• Uncertainty quantification