{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,17]],"date-time":"2026-09-17T02:32:19Z","timestamp":1789612339456,"version":"build-2803163510"},"reference-count":75,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2023,2,24]],"date-time":"2023-02-24T00:00:00Z","timestamp":1677196800000},"content-version":"vor","delay-in-days":327,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,7,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>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.<\/jats:p>","DOI":"10.1111\/rssb.12500","type":"journal-article","created":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T02:30:37Z","timestamp":1649039437000},"page":"997-1022","source":"Crossref","is-referenced-by-count":41,"title":["Robust Generalised Bayesian Inference for Intractable Likelihoods"],"prefix":"10.1093","volume":"84","author":[{"given":"Takuo","family":"Matsubara","sequence":"first","affiliation":[{"name":"Newcastle University , Newcastle upon Tyne , UK"},{"name":"The Alan Turing Institute , London , UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jeremias","family":"Knoblauch","sequence":"additional","affiliation":[{"name":"The Alan Turing Institute , London , UK"},{"name":"University College London , London , UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fran\u00e7ois-Xavier","family":"Briol","sequence":"additional","affiliation":[{"name":"The Alan Turing Institute , London , UK"},{"name":"University College London , London , UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chris J.","family":"Oates","sequence":"additional","affiliation":[{"name":"Newcastle University , Newcastle upon Tyne , UK"},{"name":"The Alan Turing Institute , London , UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2022,4,3]]},"reference":[{"key":"2023022408351585100_","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1090\/conm\/203\/02554","article-title":"Information geometry","volume":"203","author":"Amari","year":"1997","journal-title":"Contemporary Mathematics"},{"issue":"2","key":"2023022408351585100_","doi-asserted-by":"crossref","first-page":"697","DOI":"10.1214\/07-AOS574","article-title":"The pseudo-marginal approach for efficient Monte Carlo computations","volume":"37","author":"Andrieu","year":"2009","journal-title":"The Annals of Statistics"},{"issue":"6","key":"2023022408351585100_","doi-asserted-by":"crossref","first-page":"3699","DOI":"10.1214\/20-AOS1948","article-title":"Robust Bayes-like estimation: Rho-Bayes estimation","volume":"48","author":"Baraud","year":"2020","journal-title":"The Annals of Statistics"},{"key":"2023022408351585100_","volume-title":"Minimum Stein discrepancy estimators","author":"Barp","year":"2019"},{"issue":"153","key":"2023022408351585100_","first-page":"1","article-title":"Automatic differentiation in machine learning: a survey","volume":"18","author":"Baydin","year":"2018","journal-title":"Journal of Machine Learning Research"},{"issue":"4","key":"2023022408351585100_","doi-asserted-by":"crossref","first-page":"2025","DOI":"10.1093\/genetics\/162.4.2025","article-title":"Approximate Bayesian computation in population genetics","volume":"162","author":"Beaumont","year":"2002","journal-title":"Genetics"},{"issue":"1","key":"2023022408351585100_","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1007\/BF02562676","article-title":"An overview of robust Bayesian analysis","volume":"3","author":"Berger","year":"1994","journal-title":"TEST: An Official Journal of the Spanish Society of Statistics and Operations Research"},{"key":"2023022408351585100_","volume-title":"Bayesian theory","author":"Bernardo","year":"2009"},{"issue":"2","key":"2023022408351585100_","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1111\/j.2517-6161.1974.tb00999.x","article-title":"Spatial interaction and the statistical analysis of lattice systems","volume":"36","author":"Besag","year":"1974","journal-title":"Journal of the Royal Statistical Society. 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