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CATEGORIES:Applied Mathematics Seminar Series
SUMMARY:Scaling Limits in Computational Bayesian Inversion
- Claudia Schillings (Warwick)
DTSTART:20150205T160000Z
DTEND:20150205T170000Z
UID:TALK1608AT
URL:/talk/index/1608
DESCRIPTION:In this talk\, we will discuss a parametric determ
inistic formulation of Bayesian inverse problems w
ith distributed parameter uncertainty from infinit
e dimensional\, separable Banach spaces\, with uni
form prior probability measure on the uncertain pa
rameter. The underlying forward problems are param
etric\, deterministic operator equations\, and com
putational Bayesian inversion is to evaluate expec
tations of quantities of interest under the Bayesi
an posterior\, conditional on given noisy observat
ional data.\n\nFor forward problems belonging to a
certain sparsity class\, we quantify analytic reg
ularity of the Bayesian posterior and prove that t
he parametric\, deterministic density of the Bayes
ian posterior belongs to the same sparsity class.
These results suggest in particular dimension-inde
pendent convergence rates for data-adaptive Smolya
k integration algorithms\, but the error bounds de
pend exponentially on the inverse of the covarianc
e of the additive\, Gaussian observation noise. We
will discuss asymptotic expansions of the Bayesia
n estimates\, which can be used to construct quadr
ature methods combined with a curvature-based repa
rametrization of the parametric Bayesian posterior
density near the (assumed unique) global maximum
of the posterior density leading to convergence wi
th rates independent of the number of parameters a
s well as of the observation noise variance.\n
LOCATION:Poynting Small Lecture Theatre
CONTACT:Alexandra Tzella
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