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2019

On the well-posedness of Bayesian inverse problems

Latz, Jonas

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The subject of this article 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 contexts.
Our concept simply replaces the Lipschitz continuity of the posterior measure in the Hellinger distance by continuity in an appropriate distance between probability measures.

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J. Hadamard
1902
Earlier work this paper cites.
B. Sprungk
Original
1906
Earlier work this paper cites.
E. Hellinger
1909
Earlier work this paper cites.
Y. V. Prokhorov
1956
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G. R. Richter
1981
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V. I. Bogachev
1998
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R. B. Ash and C. A. Doléans-Dade
2000
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A. L. Gibbs and F. E. Su
2002
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P. McCullagh
2002
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A. L. Gibbs
2004
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D. Leao Jr, M. Fragoso, and P. Ruffino
2004
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G. Chavent
2009
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C. Villani
2009
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