5942
2016
2016
eng
reportzib
0
--
--
--
Well-posed Bayesian inverse problems and heavy-tailed stable Banach space priors
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.
urn:nbn:de:0297-zib-59422
10.3934/ipi.2017040
1438-0064
Appeared in: Inverse Problems and Imaging
no
T. J. Sullivan
Tim Sullivan
ZIB-Report
16-30
eng
uncontrolled
Bayesian inverse problems
eng
uncontrolled
heavy-tailed distribution
eng
uncontrolled
Karhunen–Loève expansion
eng
uncontrolled
stable distribution
eng
uncontrolled
uncertainty quantification
eng
uncontrolled
well-posedness
MEASURE AND INTEGRATION (For analysis on manifolds, see 58-XX)
PARTIAL DIFFERENTIAL EQUATIONS
PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX)
STATISTICS
NUMERICAL ANALYSIS
Numerical Mathematics
Sullivan, Tim
no-project
Uncertainty Quantification
https://opus4.kobv.de/opus4-zib/files/5942/stable_bip.pdf