Bayesian Linear Inverse Problems in Regularity Scales with Discrete Observations
Dong Yan,
Shota Gugushvili,
Aad van der Vaart
Abstract:We obtain rates of contraction of posterior distributions in inverse problems with discrete observations. In a general setting of smoothness scales we derive abstract results for general priors, with contraction rates determined by discrete 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… Show more
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