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SUMMARY:Metropolis-Hastings algorithms for Bayesian inference in Hilbert s
 paces - Björn Sprungk (Universität Mannheim )
DTSTART:20180227T140000Z
DTEND:20180227T160000Z
UID:TALK102103@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:In this talk we consider the Bayesian approach to inverse prob
 lems and infer uncertain coefficients in elliptic PDEs given noisy observa
 tions of the associated solution. After provinding a short introduction to
  this approach and illustrating it at a real-world groundwater flow proble
 m\, we focus on Metropolis-Hastings (MH) algorithms for approximate sampli
 ng of the resulting posterior distribution. These methods used to suffer f
 rom a high dimensional state space or a highly concentrated posterior meas
 ure\, respectively.  <br><br>In recent years dimension-independent MH algo
 rithms have been developed and analyzed\, suitable for Bayesian inference 
 in infinite dimensions. However\, the second issue of a concetrated poster
 ior has drawn less attention in the study of MH algorithms yet\, despite i
 ts importance in application.  <br><br>We present a MH algorithm well-defi
 ned in Hilbert spaces which possesses both desirable properties: a dimensi
 on-independent performance as well as a robust behaviour w.r.t. small nois
 e levels in the observational data. Moreover\, we show a first analysis of
  the noise-independence of MH algorithms in terms of the expected acceptan
 ce rate and the expected squared jump distance of the resulting Markov cha
 ins. Numerical experiments confirm the theoretical results and also indica
 te that they hold in more general situations than proven.  <br><br><br><br
 >
LOCATION:Seminar Room 2\, Newton Institute
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