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PRODID:-//Memento EPFL//
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SUMMARY:On the well-posedness of Bayesian inverse problems
DTSTART:20200211T141500
DTEND:20200211T151500
DTSTAMP:20260510T105906Z
UID:1b39b26efd17e017bbc1fa539d4afdf1f0422934ebe8aa1600dccc34
CATEGORIES:Conferences - Seminars
DESCRIPTION:    Mr. Jonas Latz    \nComputational Mathematics Semin
 ar \n\nThe subject of this talk is the introduction of a new concept of we
 ll-posedness of Bayesian inverse problems. The conventional concept of (Li
 pschitz\, Hellinger) well-posedness in [Stuart 2010\, Acta Numerica 19\, p
 p. 451-559] is difficult to verify in practice and may be inappropriate in
  some contexts. Our concept simply replaces the Lipschitz continuity of th
 e posterior measure in the Hellinger distance by continuity in an appropri
 ate distance between probability measures. Aside from the Hellinger distan
 ce\, we investigate well-posedness with respect to weak convergence\, the 
 total variation distance\, the Wasserstein distance\, and also the Kullbac
 k-Leibler divergence. We demonstrate that the weakening to continuity is t
 olerable and that the generalisation to other distances is important. The 
 main results of this article are proofs of well-posedness with respect to 
 some of the aforementioned distances for large classes of Bayesian inverse
  problems. Here\, little or no information about the underlying model is n
 ecessary\; making these results particularly interesting for practitioners
  using black-box models. We illustrate our findings with numerical example
 s motivated from machine learning and image processing.
LOCATION:MA A3 31 https://plan.epfl.ch/?room==MA%20A3%2031
STATUS:CONFIRMED
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