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

• URL: http://arxiv.org/abs/2202.04744v1
• Date: Wed, 9 Feb 2022 22:12:19 GMT
• Title: Robust Bayesian Inference for Simulator-based Models via the MMD Posterior Bootstrap
• Authors: Charita Dellaporta, Jeremias Knoblauch, Theodoros Damoulas, Fran\c{c}ois-Xavier Briol
• Abstract summary: 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 properties. The approach is then assessed on a range of examples including a g-and-k distribution and a toggle-switch model.
• Score: 13.448658162594604
• License: http://creativecommons.org/licenses/by/4.0/
• 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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