Bayesian-MICE (tBayes-MICE)

Bayesian Multiple Imputation by Chained Equations for uncertainty-aware imputation of time-series data

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Overview

Missing data are pervasive in real-world time-series applications, particularly in environmental monitoring and healthcare, where reliable uncertainty quantification is essential. tBayes-MICE extends classical MICE by replacing deterministic regression updates with Bayesian regression models whose parameters and imputations are jointly sampled via Markov Chain Monte Carlo (MCMC). The method support Random Walk Metropolis (RWM) sampling, with theoretically motivated optimal scaling to improve convergence and mixing.

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Repository Structure

Bayesian-MICE/
├── Datasets/
│   ├── AirQualityUCI.csv
│   ├── Data_subset_AirQuality.csv
│   ├── Data_with_missing_AirQuality.csv
│   ├── physionet_5000patients.csv
│   ├── physio_subdata.csv
│   └── physio_with_missing.csv
│
├── MCMC_MICE_codes/
│   ├── placeholder.py
│   ├── PhysioData_Loader.py
│   ├── MCMC_CHAIN.py
│   ├── SimpleMCMC.py
│   ├── Run_Single_MCMC.py
│   ├── Comparison_runs.py
│   ├── Run_experiments.py
│   ├── Visualisation.py
│   ├── BRITS.py
│   └── packages.py
│
├── AirQuality_Plots/
├── PhysioNet_Plots/
├── requirements.txt
└── README.md

File descriptions

File	Description
Datasets/AirQualityUCI.csv	Original AirQuality data (hourly, unprocessed)
Datasets/Data_subset_AirQuality.csv	AirQuality after removing original NaNs
Datasets/Data_with_missing_AirQuality.csv	AirQuality with artificial missing values for evaluation
Datasets/physionet_5000patients.csv	PhysioNet tabular data, filtered to rows with ≤60% missingness
Datasets/physio_subdata.csv	PhysioNet after removing all NaNs
Datasets/physio_with_missing.csv	PhysioNet with artificial missing values
MCMC_MICE_codes/placeholder.py	Missing value initialisation (mean-based and time-aware variants)
MCMC_MICE_codes/PhysioData_Loader.py	Converts raw PhysioNet data to structured format and applies missingness masks
MCMC_MICE_codes/MCMC_CHAIN.py	MCMC samplers — Random Walk Metropolis (RWM)
MCMC_MICE_codes/SimpleMCMC.py	Lagged predictor construction and parallel MCMC chains
MCMC_MICE_codes/Run_Single_MCMC.py	Runs MCMC within each MICE iteration and checks convergence
MCMC_MICE_codes/Comparison_runs.py	30-run multiple imputation comparison across all methods
MCMC_MICE_codes/Run_experiments.py	Full experimental workflow manager
MCMC_MICE_codes/Visualisation.py	Generates all figures used in the paper
MCMC_MICE_codes/BRITS.py	BRITS baseline implementation using pypots
MCMC_MICE_codes/packages.py	Full list of packages used

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Installation

1. Clone the repository

git clone https://github.com/sydney-machine-learning/Bayesian-MICE.git
cd Bayesian-MICE

2. Create a virtual environment (recommended)

python -m venv venv
source venv/bin/activate        # Linux / macOS
venv\Scripts\activate           # Windows

3. Install dependencies

pip install -r requirements.txt

Or install manually:

pip install numpy pandas scikit-learn matplotlib arviz scipy pypots

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Datasets

AirQuality (UCI)

• Source: UCI Machine Learning Repository — Air Quality Dataset
• Description: Hourly air quality measurements from an Italian city, March 2004 to February 2005
• Variables: CO, NO2, NOx, O3, temperature, humidity (15 columns)
• Missing rate: ~11% naturally occurring, plus artificially masked values for evaluation

PhysioNet

• Source: PhysioNet Challenge 2012
• Description: ICU patient records, 48-hour time series of 37 clinical variables
• Processing: Filtered to 5000 patients; rows with more than 60% missingness removed
• Missing rate: Varies by variable (10–80%)

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Reproducing the Experiments

Step 1 — Prepare the data

python MCMC_MICE_codes/PhysioData_Loader.py

Outputs:

• Datasets/physio_subdata.csv
• Datasets/physio_with_missing.csv

Step 2 — Run comparison across methods

python MCMC_MICE_codes/Comparison_runs.py

Compares tBayes-MICE, MICE and BRITS over 30 runs.

Step 3 — Run the full experiment

python MCMC_MICE_codes/Run_experiments.py

Runs all methods on both datasets over 30 independent runs.

Step 4 — Generate plots

python MCMC_MICE_codes/Visualisation.py

Reproduces all figures from the paper. Output saved to AirQuality_Plots/ and PhysioNet_Plots/.

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Reproducibility

Item	Detail
Random seed	Fixed at 42 across all experiments
Number of runs	30 independent runs per method
Hardware	UNSW Katana HPC cluster
HPC citation	DOI: 10.26190/669XA286
Python version	3.8+
OS	Linux (Ubuntu 20.04)

Results may vary slightly on different hardware due to floating-point precision differences. Reported metrics are means over 30 runs to account for this variability.

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Results Summary

Performance on AirQuality dataset (MAE, lower is better):

Method	MAE	RMSE
MICE (classical)	—	—
tBayes-MICE V1	—	—
BRITS	—	—

Full results with confidence intervals are reported in the paper.

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Citation

If you use this code or results in your work, please cite:

@article{ibenegbu2026tbayes,
  title={tBayes-MICE: A Bayesian Approach to Multiple Imputation for Time Series Data},
  author={Ibenegbu, Amuche and de Micheaux, Pierre Lafaye and Chandra, Rohitash},
  journal={arXiv preprint arXiv:2603.27142},
  year={2026}
  url     = {https://arxiv.org/abs/2603.27142}
}

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Issues and Contributions

• Found a bug? Open an issue
• Want to contribute? Fork the repository and submit a pull request

Experiments were run on the Katana High Performance Computing cluster, supported by Research Technology Services at UNSW Sydney.