• search hit 3 of 23
Back to Result List

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.

Download full text files

Export metadata

Additional Services

Share in Twitter Search Google Scholar
Metadaten
Author:T. J. Sullivan
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