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

DOI10.1137/18M1226269zbMath1436.62161arXiv1811.04058OpenAlexW3007421735MaRDI QIDQ4960994

Hanne Kekkonen, Matteo Giordano

Publication date: 24 April 2020

Published in: SIAM/ASA Journal on Uncertainty Quantification (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.04058

zbMATH Keywords

elliptic partial differential equationsGaussian priorsasymptotics of nonparametric Bayes proceduresBernstein-von Mises theoremsTikhonov regularizers

Mathematics Subject Classification ID

Asymptotic properties of nonparametric inference (62G20) Boundary value problems for second-order elliptic equations (35J25) Heat equation (35K05) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21)

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A Bernstein–von-Mises theorem for the Calderón problem with piecewise constant conductivities ⋮ Consistency of Bayesian inference with Gaussian process priors for a parabolic inverse problem ⋮ Dimension Free Nonasymptotic Bounds on the Accuracy of High-Dimensional Laplace Approximation ⋮ Are Minimizers of the Onsager–Machlup Functional Strong Posterior Modes? ⋮ Convergence Rates for Learning Linear Operators from Noisy Data ⋮ Re-thinking high-dimensional mathematical statistics. Abstracts from the workshop held May 15--21, 2022 ⋮ Error control of the numerical posterior with Bayes factors in Bayesian uncertainty quantification ⋮ Nonparametric statistical inference for drift vector fields of multi-dimensional diffusions ⋮ On some information-theoretic aspects of non-linear statistical inverse problems ⋮ Solving inverse problems using data-driven models ⋮ Statistical guarantees for Bayesian uncertainty quantification in nonlinear inverse problems with Gaussian process priors ⋮ Bernstein-von Mises theorems for statistical inverse problems. II: Compound Poisson processes ⋮ Non-asymptotic error estimates for the Laplace approximation in Bayesian inverse problems

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