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

Charita Dellaporta; Jeremias Knoblauch; Theodoros Damoulas; François-Xavier Briol

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arXiv · 2202.04744

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

Charita Dellaporta·Jeremias Knoblauch·Theodoros Damoulas·François-Xavier Briol

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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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BibTeX RIS

Charita Dellaporta, Jeremias Knoblauch, Theodoros Damoulas, François-Xavier Briol. 2022-02-09. Robust Bayesian Inference for Simulator-based Models via the MMD Posterior Bootstrap. https://arxiv.org/abs/2202.04744

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