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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Metropolis-Hastings algorithms for Bayesian infere
nce in Hilbert spaces - Björn Sprungk (Universität
Mannheim )
DTSTART;TZID=Europe/London:20180227T140000
DTEND;TZID=Europe/London:20180227T160000
UID:TALK102103AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/102103
DESCRIPTION:In this talk we consider the Bayesian approach to
inverse problems and infer uncertain coefficients
in elliptic PDEs given noisy observations of the a
ssociated solution. After provinding a short intro
duction to this approach and illustrating it at a
real-world groundwater flow problem\, we focus on
Metropolis-Hastings (MH) algorithms for approximat
e sampling of the resulting posterior distribution
. These methods used to suffer from a high dimensi
onal state space or a highly concentrated posterio
r measure\, respectively.

In recent years
dimension-independent MH algorithms have been dev
eloped and analyzed\, suitable for Bayesian infere
nce in infinite dimensions. However\, the second i
ssue of a concetrated posterior has drawn less att
ention in the study of MH algorithms yet\, despite
its importance in application.

We presen
t a MH algorithm well-defined in Hilbert spaces wh
ich possesses both desirable properties: a dimensi
on-independent performance as well as a robust beh
aviour w.r.t. small noise levels in the observatio
nal data. Moreover\, we show a first analysis of t
he noise-independence of MH algorithms in terms of
the expected acceptance rate and the expected squ
ared jump distance of the resulting Markov chains.
Numerical experiments confirm the theoretical res
ults and also indicate that they hold in more gene
ral situations than proven.

LOCATION:Seminar Room 2\, Newton Institute
CONTACT:info@newton.ac.uk
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