Bayesian experimental design: grouped geometric pooled posterior via ensemble Kalman methods

2026-04-20

AI Summary

This work addresses the challenge in Bayesian experimental design where nested inference struggles to balance computational efficiency and estimation accuracy under strong posterior heterogeneity. The authors propose a grouped geometric pooling posterior framework that constructs shared proposal distributions by grouping outer-level samples, thereby improving the accuracy of expected information gain (EIG) estimation at amortized computational cost. This approach is further enhanced by an ensemble Kalman inversion (EKI) sampling mechanism that incurs no additional forward simulations, reducing overall computational overhead. A conservative diagnostic metric is introduced to guide grouping strategies and ensure robustness. Demonstrated on both Gaussian-linear models and high-dimensional network bias calibration tasks, the method significantly outperforms conventional amortized approaches, yielding more accurate and stable EIG estimates at comparable computational expense.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Probabilistic Inference

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Bayesian experimental design (BED) for complex physical systems is often limited by the nested inference required to estimate the expected information gain (EIG) or its gradients. Each outer sample induces a different posterior, creating a large and heterogeneous set of inference targets. Existing methods have to sacrifice either accuracy or efficiency: they either perform per-outer-sample posterior inference, which yields higher fidelity but at prohibitive computational cost, or amortize the inner inference across all outer samples for computational reuse, at the risk of degraded accuracy under posterior heterogeneity. To improve accuracy and maintain cost at the amortized level, we propose a grouped geometric pooled posterior framework that partitions outer samples into groups and constructs a pooled proposal for each group. While such grouping strategy would normally require generating separate proposal samples for different groups, our tailored ensemble Kalman inversion (EKI) formulation generates these samples without extra forward-model evaluation cost. We also introduce a conservative diagnostic to assess importance-sampling quality to guide grouping. This grouping strategy improves within-group proposal-target alignment, yielding more accurate and stable estimators while keeping the cost comparable to amortized approaches. We evaluate the performance of our method on both Gaussian-linear and high-dimensional network-based model discrepancy calibration problems.

Problem

• Bayesian experimental design
• expected information gain
• posterior heterogeneity
• nested inference
• amortized inference

Innovation

• Bayesian experimental design
• grouped geometric pooling
• ensemble Kalman inversion
• expected information gain
• amortized inference