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Robust generalised Bayesian inference for intractable likelihoods

Matsubara, Takuo; Knoblauch, Jeremias; Briol, François‐Xavier; Oates, Chris J; (2022) Robust generalised Bayesian inference for intractable likelihoods. Journal of the Royal Statistical Society: Series B 10.1111/rssb.12500. (In press). Green open access

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Abstract

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.

Type: Article
Title: Robust generalised Bayesian inference for intractable likelihoods
Open access status: An open access version is available from UCL Discovery
DOI: 10.1111/rssb.12500
Publisher version: https://doi.org/10.1111/rssb.12500
Language: English
Additional information: © 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. This is an open access article under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/).
Keywords: intractable likelihood, kernel methods, robust statistics, Stein's method
UCL classification: UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL
URI: https://discovery.ucl.ac.uk/id/eprint/10146902
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