We consider the well-posedness of Bayesian inverse problems when the prior
belongs to the class of convex measures. This class includes the Gaussian and
Besov measures as well as certain classes of hierarchical priors. We identify
appropriate conditions on the likelihood distribution and the prior measure
which guarantee existence, uniqueness and stability of the posterior measure
with respect to perturbations of the data. We also consider convergence of
numerical approximations of the posterior given a consistent discretization.
Finally, we present a general recipe for construction of convex priors on
Banach spaces which will be of interest in practical applications where one
often works with spaces such as L2 or the continuous functions.
%0 Generic
%1 hosseini2016wellposed
%A Hosseini, Bamdad
%A Nigam, Nilima
%D 2016
%K bayesian tutorial
%T Well-posed Bayesian Inverse Problems: beyond Gaussian priors
%U http://arxiv.org/abs/1604.02575
%X We consider the well-posedness of Bayesian inverse problems when the prior
belongs to the class of convex measures. This class includes the Gaussian and
Besov measures as well as certain classes of hierarchical priors. We identify
appropriate conditions on the likelihood distribution and the prior measure
which guarantee existence, uniqueness and stability of the posterior measure
with respect to perturbations of the data. We also consider convergence of
numerical approximations of the posterior given a consistent discretization.
Finally, we present a general recipe for construction of convex priors on
Banach spaces which will be of interest in practical applications where one
often works with spaces such as L2 or the continuous functions.
@misc{hosseini2016wellposed,
abstract = {We consider the well-posedness of Bayesian inverse problems when the prior
belongs to the class of convex measures. This class includes the Gaussian and
Besov measures as well as certain classes of hierarchical priors. We identify
appropriate conditions on the likelihood distribution and the prior measure
which guarantee existence, uniqueness and stability of the posterior measure
with respect to perturbations of the data. We also consider convergence of
numerical approximations of the posterior given a consistent discretization.
Finally, we present a general recipe for construction of convex priors on
Banach spaces which will be of interest in practical applications where one
often works with spaces such as L2 or the continuous functions.},
added-at = {2016-04-12T05:49:44.000+0200},
author = {Hosseini, Bamdad and Nigam, Nilima},
biburl = {https://www.bibsonomy.org/bibtex/27e8ab0493bcd2bb4a498eeae18019908/pixor},
description = {() - 1604.02575v1.pdf},
interhash = {53549f5acc16dd2d3d02e560e311d306},
intrahash = {7e8ab0493bcd2bb4a498eeae18019908},
keywords = {bayesian tutorial},
note = {cite arxiv:1604.02575v1.pdf},
timestamp = {2016-04-12T05:49:44.000+0200},
title = {Well-posed Bayesian Inverse Problems: beyond Gaussian priors},
url = {http://arxiv.org/abs/1604.02575},
year = 2016
}