Robust Bayesian Inference for Simulator-based Models via the MMD Posterior Bootstrap

2022/02/09 by Charita Dellaporta, Dellaporta, Charita, Jeremias Knoblauch +5 · 8 citations
Decision Sciences · Mathematics · Physics and Astronomy · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Methodology (stat.ME) #Model Reduction and Neural Networks #Simulation Techniques and Applications #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.2202.04744

openalex publication_date 2022/02/09 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

Simulator-based models are models for which the likelihood is intractable but simulation of synthetic data is possible. They are often used to describe complex real-world phenomena, and as such can often be misspecified in practice. Unfortunately, existing Bayesian approaches for simulators are known to perform poorly in those cases. In this paper, we propose a novel algorithm based on the posterior bootstrap and maximum mean discrepancy estimators. This leads to a highly-parallelisable Bayesian inference algorithm with strong robustness properties. This is demonstrated through an in-depth theoretical study which includes generalisation bounds and proofs of frequentist consistency and robustness of our posterior. The approach is then assessed on a range of examples including a g-and-k distribution and a toggle-switch model.

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