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SUMMARY:Statistical guarantees for Bayesian uncertainty quantification in 
 inverse problems - Richard Nickl (University of Cambridge)
DTSTART:20180409T133000Z
DTEND:20180409T140000Z
UID:TALK103543@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:We discuss recent results in mathematical statistics that prov
 ide objective statistical guarantees for Bayesian algorithms in (possibly 
 non-linear) noisy inverse problems. We focus in particular on the justific
 ation of Bayesian credible sets as proper frequentist confidence sets in t
 he small noise limit via so-called `Bernstein - von Mises theorems&#39\;\,
  which provide Gaussian approximations to the posterior distribution\, and
  introduce notions of such theorems in the infinite-dimensional settings r
 elevant for inverse problems. We discuss in detail such a Bernstein-von Mi
 ses result for Bayesian inference on the unknown potential in the Schroedi
 nger equation from an observation of the solution of that PDE corrupted by
  additive Gaussian white noise.  See https://arxiv.org/abs/1707.01764  and
  also  https://arxiv.org/abs/1708.06332
LOCATION:Seminar Room 1\, Newton Institute
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