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CATEGORIES:Statistics
SUMMARY:Posterior contraction rates for potentially nonlin
ear inverse problems - Sergios Agapiou\, Universit
y of Cyprus
DTSTART;TZID=Europe/London:20200214T140000
DTEND;TZID=Europe/London:20200214T150000
UID:TALK135961AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/135961
DESCRIPTION:We will consider a family of potentially nonlinear
inverse problems subject to Gaussian additive whi
te noise. We will assume truncated Gaussian prior
s and our interest will be in studying the asympto
tic performance of the Bayesian posterior in the s
mall noise limit. In particular\, we will develop
a theory for obtaining posterior contraction rates
. The theory is based on the techniques of Knapik
and Salomond 2018\, which show how to derive poste
rior contraction rates for inverse problems\, usin
g rates of contraction for direct problems and the
notion of the modulus of continuity. We will work
under the assumption that the forward operator ca
n be associated to a linear operator in a certain
sense. We will present techniques from regularizat
ion theory\, which allow both to bound the modulus
of continuity\, as well as to derive optimal rate
s of contraction for the direct problem by appropr
iately tuning the prior-truncation level. Finally\
, we will combine to obtain optimal rates of contr
action for a range of inverse problems.\n\nThis is
joint work with Peter MathÃ© (Weierstrass Institut
e\, Berlin)
LOCATION:MR12
CONTACT:Dr Sergio Bacallado
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