%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 }