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SUMMARY:Posterior contraction rates for potentially nonlinear inverse prob
 lems - Sergios Agapiou\, University of Cyprus
DTSTART:20200214T140000Z
DTEND:20200214T150000Z
UID:TALK135961@talks.cam.ac.uk
CONTACT:Dr Sergio Bacallado
DESCRIPTION:We will consider a family of potentially nonlinear inverse pro
 blems subject to Gaussian additive white noise.  We will assume truncated 
 Gaussian priors and our interest will be in studying the asymptotic perfor
 mance of the Bayesian posterior in the small noise limit. In particular\, 
 we will develop a theory for obtaining posterior contraction rates. The th
 eory is based on the techniques of Knapik and Salomond 2018\, which show h
 ow to derive posterior contraction rates for inverse problems\, using rate
 s of contraction for direct problems and the notion of the modulus of cont
 inuity. We will work under the assumption that the forward operator can be
  associated to a linear operator in a certain sense. We will present techn
 iques from regularization theory\, which allow both to bound the modulus o
 f continuity\, as well as to derive optimal rates of contraction for the d
 irect problem by appropriately tuning the prior-truncation level. Finally\
 , we will combine to obtain optimal rates of contraction for a range of in
 verse problems.\n\nThis is joint work with Peter Mathé (Weierstrass Insti
 tute\, Berlin)
LOCATION:MR12
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