Well-posed Bayesian inverse problems and heavy-tailed stable Banach space priors
Please always quote using this URN: urn:nbn:de:0297-zib-59422
- This article extends the framework of Bayesian inverse problems in infinite-dimensional parameter spaces, as advocated by Stuart (Acta Numer. 19:451–559, 2010) and others, to the case of a heavy-tailed prior measure in the family of stable distributions, such as an infinite-dimensional Cauchy distribution, for which polynomial moments are infinite or undefined. It is shown that analogues of the Karhunen–Loève expansion for square-integrable random variables can be used to sample such measures. Furthermore, under weaker regularity assumptions than those used to date, the Bayesian posterior measure is shown to depend Lipschitz continuously in the Hellinger metric upon perturbations of the misfit function and observed data.
Author: | T. J. Sullivan |
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Document Type: | ZIB-Report |
Tag: | Bayesian inverse problems; Karhunen–Loève expansion; heavy-tailed distribution; stable distribution; uncertainty quantification; well-posedness |
MSC-Classification: | 28-XX MEASURE AND INTEGRATION (For analysis on manifolds, see 58-XX) |
35-XX PARTIAL DIFFERENTIAL EQUATIONS | |
60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) | |
62-XX STATISTICS | |
65-XX NUMERICAL ANALYSIS | |
Year of first publication: | 2016 |
Series (Serial Number): | ZIB-Report (16-30) |
ISSN: | 1438-0064 |
Published in: | Appeared in: Inverse Problems and Imaging |
DOI: | https://doi.org/10.3934/ipi.2017040 |