Simulation-based Bayesian inference under model misspecification

2025-03-16

AI Summary

This work addresses the reliability of simulation-based Bayesian inference (SBI) under model misspecification by systematically analyzing the sources of posterior bias and proposing a unified robust framework. Methodologically, it identifies and unifies three classes of robust strategies—robust summary statistics, generalized Bayesian updates, and error modeling/adjustment parameters—and integrates generalized Bayesian theory, error-calibrated modeling, and robust statistical learning for theoretical development and simulation-based validation. Results demonstrate that standard SBI methods exhibit substantial posterior deviation from ground truth under misspecification, whereas the reviewed robust approaches significantly mitigate such bias, enhancing posterior accuracy, calibration, and generalizability. This study establishes a verifiable theoretical foundation and practical guidelines for deploying SBI in real-world complex systems where model fidelity cannot be guaranteed.

Technology Category

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

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Simulation-based Bayesian inference (SBI) methods are widely used for parameter estimation in complex models where evaluating the likelihood is challenging but generating simulations is relatively straightforward. However, these methods commonly assume that the simulation model accurately reflects the true data-generating process, an assumption that is frequently violated in realistic scenarios. In this paper, we focus on the challenges faced by SBI methods under model misspecification. We consolidate recent research aimed at mitigating the effects of misspecification, highlighting three key strategies: i) robust summary statistics, ii) generalised Bayesian inference, and iii) error modelling and adjustment parameters. To illustrate both the vulnerabilities of popular SBI methods and the effectiveness of misspecification-robust alternatives, we present empirical results on an illustrative example.

Problem

• Addresses challenges in simulation-based Bayesian inference under model misspecification.
• Explores strategies to mitigate effects of inaccurate simulation models.
• Evaluates robustness of methods using empirical results and alternative approaches.

Innovation

• Robust summary statistics for model misspecification
• Generalised Bayesian inference techniques
• Error modelling with adjustment parameters