Bayesian learning strategies for reducing uncertainty of decision-making in case of missing values

Background: Liquidity crises pose significant risks to financial stability, and missing data in predictive models increase the uncertainty in decision-making. This study aims to develop a robust Bayesian Model Averaging (BMA) framework using decision trees (DTs) to enhance liquidity crisis prediction under missing data conditions, offering reliable probabilistic estimates and insights into uncertainty. Methods: We propose a BMA framework over DTs, employing Reversible Jump Markov Chain Monte Carlo (RJ MCMC) sampling with a sweeping strategy to mitigate overfitting. Three preprocessing techniques for missing data were evaluated: Cont (treating variables as continuous with missing values labeled by a constant), ContCat (converting variables with missing values to categorical), and Ext (extending features with binary missing-value indicators). Results: The Ext method achieved 100% accuracy on a synthetic dataset and 92.2% on a real-world dataset of 20,000 companies (11% in crisis), outperforming baselines (AUC PRC 0.817 vs. 0.803, p < 0.05). The framework provided interpretable uncertainty estimates and identified key financial indicators driving crisis predictions. Conclusions: The BMA-DT framework with the Ext technique offers a scalable, interpretable solution for handling missing data, improving prediction accuracy and uncertainty estimation in liquidity crisis forecasting, with potential applications in finance, healthcare, and environmental modeling.