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math.ST2012★ 37 cited
Bayesian Posterior Contraction Rates for Linear Severely Ill-posed Inverse Problems
Sergios Agapiou, Andrew M. Stuart, Yuan-Xiang Zhang
We consider a class of linear ill-posed inverse problems arising from inversion of a compact operator with singular values which decay exponentially to zero. We adopt a Bayesian ap…
math.ST2012★ 87 cited
Posterior Contraction Rates for the Bayesian Approach to Linear Ill-Posed Inverse Problems
Sergios Agapiou, Stig Larsson, Andrew M. Stuart
We consider a Bayesian nonparametric approach to a family of linear inverse problems in a separable Hilbert space setting with Gaussian noise. We assume Gaussian priors, which are…