BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Björn Sprungk (TU Freiberg\, DE) DTSTART:20200629T130000Z DTEND:20200629T134500Z DTSTAMP:20260423T022738Z UID:OWMADS/12 DESCRIPTION:Title: Noise-level robust Monte Carlo methods for Bayesian inference with infomat ive data\nby Björn Sprungk (TU Freiberg\, DE) as part of One World se minar: Mathematical Methods for Arbitrary Data Sources (MADS)\n\n\nAbstrac t\nThe Bayesian approach to inverse problems provides a rigorous framework for the incorporation and quantification of uncertainties in measurements \, parameters and models. However\, sampling from or integrating w.r.t. th e resultung posterior measure can become computationally challenging. In r ecent years\, a lot of effort has been spent on deriving dimension-indepen dent methods and to combine efficient sampling strategies with multilevel or surrogate methods in order to reduce the computational burden of Bayesi an inverse problems.\nIn this talk\, we are interested in designing numeri cal methods which are robust w.r.t. the size of the observational noise\, i.e.\, methods which behave well in case of concentrated posterior measure s. The concentration of the posterior is a highly desirable situation in p ractice\, since it relates to informative or large data. However\, it can pose as well a significant computational challenge for numerical methods b ased on the prior or reference measure. We propose to employ the Laplace a pproximation of the posterior as the base measure for numerical integratio n in this context. The Laplace approximation is a Gaussian measure centere d at the maximum a-posteriori estimate (MAPE) and with covariance matrix d epending on the Hessian of the log posterior density at the MAPE. We discu ss convergence results of the Laplace approximation in terms of the Hellin ger distance and analyze the efficiency of Monte Carlo methods based on it . In particular\, we show that Laplace-based importance sampling and quasi -Monte-Carlo as well as Laplace-based Metropolis-Hastings algorithms are r obust w.r.t. the concentration of the posterior for large classes of poste rior distributions and integrands whereas prior-based Monte Carlo sampling methods are not.\n LOCATION:https://researchseminars.org/talk/OWMADS/12/ END:VEVENT END:VCALENDAR