 Robust generalised Bayesian inference for intractable likelihoodsTakuo Matsubara, Jeremias Knoblauch, François‐Xavier Briol and Chris J. Oates Journal of the Royal Statistical Society Series B, 2022, vol. 84, issue 3, 997-1022 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. Date: 2022 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:bla:jorssb:v:84:y:2022:i:3:p:997-1022 Ordering information: This journal article can be ordered from Access Statistics for this article Journal of the Royal Statistical Society Series B is currently edited by P. Fryzlewicz and I. Van Keilegom More articles in Journal of the Royal Statistical Society Series B from Royal Statistical Society Contact information at EDIRC. |
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