Efficient Uncertainty Propagation in Bayesian Two-Step Procedures

2025-05-15

AI Summary

To address the high computational cost arising from joint propagation of aleatoric and epistemic uncertainties in Bayesian two-stage inference, this paper proposes an efficient uncertainty propagation framework. First, a representative subset is selected via Pareto-smoothed importance sampling to reduce sampling redundancy. Second, an importance-weighted moment-matching strategy is introduced for lightweight posterior approximation. Third, an iterative mixture-distribution expansion mechanism is developed to jointly model both uncertainty types within surrogate modeling and MICE-based multiple imputation. The method preserves posterior accuracy while significantly reducing the cost of multi-model fitting—achieving several-fold improvements in computational efficiency. It establishes a scalable paradigm for Bayesian inference under complex, heterogeneous uncertainty scenarios.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Uncertainty Representations
• Multiagent Systems: Multiagent Systems under Uncertainty

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Bayesian inference provides a principled framework for probabilistic reasoning. If inference is performed in two steps, uncertainty propagation plays a crucial role in accounting for all sources of uncertainty and variability. This becomes particularly important when both aleatoric uncertainty, caused by data variability, and epistemic uncertainty, arising from incomplete knowledge or missing data, are present. Examples include surrogate models and missing data problems. In surrogate modeling, the surrogate is used as a simplified approximation of a resource-heavy and costly simulation. The uncertainty from the surrogate-fitting process can be propagated using a two-step procedure. For modeling with missing data, methods like Multivariate Imputation by Chained Equations (MICE) generate multiple datasets to account for imputation uncertainty. These approaches, however, are computationally expensive, as multiple models must be fitted separately to surrogate parameters respectively imputed datasets. To address these challenges, we propose an efficient two-step approach that reduces computational overhead while maintaining accuracy. By selecting a representative subset of draws or imputations, we construct a mixture distribution to approximate the desired posteriors using Pareto smoothed importance sampling. For more complex scenarios, this is further refined with importance weighted moment matching and an iterative procedure that broadens the mixture distribution to better capture diverse posterior distributions.

Problem

• Efficient uncertainty propagation in Bayesian two-step procedures
• Reducing computational cost in surrogate modeling and missing data problems
• Accurate approximation of posteriors using subset selection and mixture distributions

Innovation

• Efficient two-step Bayesian uncertainty propagation
• Pareto smoothed importance sampling approximation
• Importance weighted moment matching refinement