BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Pierre Nyquist (Chalmers University of Technology & University of Gothenburg) DTSTART:20240221T121500Z DTEND:20240221T130000Z DTSTAMP:20260422T155052Z UID:gbgstats/42 DESCRIPTION:Title: Large deviations for Markov chain Monte Carlo methods: the surprisingly curious case of Metropolis-Hastings.\nby Pierre Nyquist (Chalmers Univ ersity of Technology & University of Gothenburg) as part of Gothenburg sta tistics seminar\n\nLecture held in MVL14.\n\nAbstract\nMarkov chain Monte Carlo (MCMC) methods have become the workhorse for numerical computations in a range of scientific disciplines\, e.g.\, computational chemistry and physics\, statistics\, and machine learning. The performance of MCMC metho ds has therefore become an important topic at the intersection of probabil ity theory and (computational) statistics: e.g.\, when the underlying dist ribution one is trying to sample from becomes sufficiently complex\, conve rgence speed and/or the cost per iteration becomes an issue for most MCMC methods. \n\nThe analysis\, and subsequently design\, of MCMC methods has to a large degree relied on classical tools used to determine the speed of convergence of Markov chains\, e.g.\, mixing times\, spectral gap and fun ctional inequalities (Poincaré\, log-Sobolev). An alternative avenue is t o use the theory of large deviations for empirical measures. In this talk I will first give a general outline of this approach to analysing MCMC met hods\, along with some recent examples. I will then consider the specific case of the Metropolis-Hastings algorithm\, the most classical amongst all MCMC methods and a foundational building block for many more advanced met hods. Despite the simplicity of this method\, it turns out that the theore tical analysis of it is still a rich area\, and from the large deviation p erspective it is surprisingly difficult to treat. As a first step we show a large deviation principle for the underlying Markov chain\, extending th e celebrated Donsker-Varadhan theory. Time permitted I will also discuss o ngoing and future work on using this result for better understanding of bo th the Metropolis-Hastings method and more advanced methods\, such as appr oximate Bayesian computation (ABC-MCMC) and the Metropolis-adjusted Langev in algorithm (MALA).\n\nThe talk will be self-contained and no prior knowl edge of either MCMC methods or large deviations is required.\n\nThe talk i s primarily based on join work with Federica Milinanni (KTH).\n LOCATION:https://researchseminars.org/talk/gbgstats/42/ END:VEVENT END:VCALENDAR