Bayesian linear inverse problems in regularity scales - VVSOR - VVSOR

Netherlands Society for Statistics and Operations Research | Dutch

Bayesian linear inverse problems in regularity scales

We cordially invite you to the next Bayes club meeting, taking place on Friday, the 6th of April, in Amsterdam (UvA, Science Park 904)

Speaker: Dong Yan (Leiden University)
Title: Bayesian linear inverse problems in regularity scales
Time: 16:00-17:00 on the 6th of April, 2018
Location: UvA, Science Park 904, room D1.115

We obtain rates of contraction of posterior distributions in inverse problems defined by scales of smoothness classes. We derive abstract results for general priors, with contraction rates determined by Galerkin approximation. The rate depends on the amount of prior concentration near the true function and the prior mass of functions with inferior Galerkin approximation. We apply the general result to non-conjugate series priors, showing that these priors give near optimal and adaptive recovery in some generality, Gaussian priors, and mixtures of Gaussian priors, where the latter are also shown to be near optimal and adaptive. The proofs are based on general testing and approximation arguments, without explicit calculations on the posterior distribution. We are thus not restricted to priors based on the singular value decomposition of the operator. We illustrate the results with examples of inverse problems resulting from differential equations.

This is a joint work with Shota Gugushvili and Aad van der Vaart.

For the list of upcoming talks and further information about the seminar please visit the (relocated) seminar website: bszabo/bayes_club