Bernstein-von Mises Theorems and Uncertainty Quantification for Linear Inverse Problems

  title={Bernstein-von Mises Theorems and Uncertainty Quantification for Linear Inverse Problems},
  author={M. Giordano and Hanne Kekkonen},
  journal={SIAM/ASA J. Uncertain. Quantification},
We consider the statistical inverse problem of recovering an unknown function $f$ from a linear measurement corrupted by additive Gaussian white noise. We employ a nonparametric Bayesian approach with standard Gaussian priors, for which the posterior-based reconstruction of $f$ corresponds to a Tikhonov regulariser $\bar f$ with a reproducing kernel Hilbert space norm penalty. We prove a semiparametric Bernstein-von Mises theorem for a large collection of linear functionals of $f$, implying… Expand
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