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SUMMARY:On the well-posedness of Bayesian inverse problems - Jonas Latz (T
 U Munich)
DTSTART:20191001T130000Z
DTEND:20191001T140000Z
UID:TALK130309@talks.cam.ac.uk
CONTACT:Carola-Bibiane Schoenlieb
DESCRIPTION:The subject of this talk is the introduction of a new concept 
 of well-posedness of Bayesian inverse problems. The conventional concept o
 f (Lipschitz\, Hellinger) well-posedness in [Stuart 2010\, Acta Numerica 1
 9\, pp. 451-559] is difficult to verify in practice and may be inappropria
 te in some contexts. Our concept simply replaces the Lipschitz continuity 
 of the posterior measure in the Hellinger distance by continuity in an app
 ropriate distance between probability measures. Aside from the Hellinger d
 istance\, we investigate well-posedness with respect to weak convergence\,
  the total variation distance\, the Wasserstein distance\, and also the Ku
 llback--Leibler divergence. We demonstrate that the weakening to continuit
 y is tolerable and that the generalisation to other distances is important
 . The main results are well-posedness statements with respect to some of t
 he aforementioned distances for large classes of Bayesian inverse problems
 . Here\, little or no information about the underlying model is necessary\
 ; making these results particularly interesting for practitioners using bl
 ack-box models. We illustrate our findings with numerical examples motivat
 ed from machine learning and image processing.
LOCATION:MR 14\, Centre for Mathematical Sciences
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