Variational posteriors for Besov-prior Bayesian inverse problems achieve minimax-optimal convergence rates matching exact posteriors under general PDE operator conditions.
Bernstein–von Mises theorems for statistical inverse problems I: Schr¨ odinger equation
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Consistency of variational inference for Besov priors in non-linear inverse problems
Variational posteriors for Besov-prior Bayesian inverse problems achieve minimax-optimal convergence rates matching exact posteriors under general PDE operator conditions.