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Robust generalised Bayesian inference for intractable likelihoods

Lookup NU author(s): Takuo Matsubara, Professor Chris Oates



This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).


© 2022 The Authors. Journal of the Royal Statistical Society: Series B (Statistical Methodology) published by John Wiley & Sons Ltd on behalf of Royal Statistical Society. Generalised Bayesian inference updates prior beliefs using a loss function, rather than a likelihood, and can therefore be used to confer robustness against possible mis-specification of the likelihood. Here we consider generalised Bayesian inference with a Stein discrepancy as a loss function, motivated by applications in which the likelihood contains an intractable normalisation constant. In this context, the Stein discrepancy circumvents evaluation of the normalisation constant and produces generalised posteriors that are either closed form or accessible using the standard Markov chain Monte Carlo. On a theoretical level, we show consistency, asymptotic normality, and bias-robustness of the generalised posterior, highlighting how these properties are impacted by the choice of Stein discrepancy. Then, we provide numerical experiments on a range of intractable distributions, including applications to kernel-based exponential family models and non-Gaussian graphical models.

Publication metadata

Author(s): Matsubara T, Knoblauch J, Briol F-X, Oates CJ

Publication type: Article

Publication status: Published

Journal: Journal of the Royal Statistical Society. Series B: Statistical Methodology

Year: 2022

Volume: 84

Issue: 3

Pages: 997-1022

Print publication date: 01/07/2022

Online publication date: 03/04/2022

Acceptance date: 25/01/2022

Date deposited: 28/04/2022

ISSN (print): 1369-7412

ISSN (electronic): 1467-9868

Publisher: John Wiley and Sons Inc.


DOI: 10.1111/rssb.12500


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