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CATEGORIES:Cambridge Image Analysis Seminars
SUMMARY:On the well-posedness of Bayesian inverse problems
- Jonas Latz (TU Munich)
DTSTART;TZID=Europe/London:20191001T140000
DTEND;TZID=Europe/London:20191001T150000
UID:TALK130309AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/130309
DESCRIPTION:The subject of this talk is the introduction of a
new concept of well-posedness of Bayesian inverse
problems. The conventional concept of (Lipschitz\,
Hellinger) well-posedness in [Stuart 2010\, Acta
Numerica 19\, pp. 451-559] is difficult to verify
in practice and may be inappropriate in some conte
xts. Our concept simply replaces the Lipschitz con
tinuity of the posterior measure in the Hellinger
distance by continuity in an appropriate distance
between probability measures. Aside from the Helli
nger distance\, we investigate well-posedness with
respect to weak convergence\, the total variation
distance\, the Wasserstein distance\, and also th
e Kullback--Leibler divergence. We demonstrate tha
t the weakening to continuity is tolerable and tha
t the generalisation to other distances is importa
nt. The main results are well-posedness statements
with respect to some of the aforementioned distan
ces for large classes of Bayesian inverse problems
. Here\, little or no information about the underl
ying model is necessary\; making these results par
ticularly interesting for practitioners using blac
k-box models. We illustrate our findings with nume
rical examples motivated from machine learning and
image processing.
LOCATION:MR 14\, Centre for Mathematical Sciences
CONTACT:Carola-Bibiane Schoenlieb
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