Designing truncated priors for direct and inverse Bayesian problems

DOI10.1214/21-EJS1966zbMath1493.62238arXiv2105.10254OpenAlexW3165874090MaRDI QIDQ2136605

Sergios Agapiou, Peter Mathé

Publication date: 11 May 2022

Published in: Electronic Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2105.10254

zbMATH Keywords

Bayesian inverse problemsrates of posterior contraction

Mathematics Subject Classification ID

Asymptotic properties of nonparametric inference (62G20) Bayesian inference (62F15) Bayesian problems; characterization of Bayes procedures (62C10) Inverse problems for integral equations (45Q05)

Related Items (3)

Convergence Rates for Learning Linear Operators from Noisy Data ⋮ Inverse learning in Hilbert scales ⋮ Nonlinear Tikhonov regularization in Hilbert scales for inverse learning

Cites Work

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• Bayesian inverse problems with non-conjugate priors
• Bayesian inverse problems with Gaussian priors
• On statistical Calderón problems
• Bernstein-von Mises theorems for statistical inverse problems. I: Schrödinger equation
• Minimax risk over hyperrectangles, and implications
• Rates of contraction of posterior distributions based on Gaussian process priors
• Convergence rates of posterior distributions for non iid observations
• Adaptive Bayesian inference on the mean of an infinite-dimensional normal distribution
• A general approach to posterior contraction in nonparametric inverse problems
• Bayesian aspects of some nonparametric problems
• Empirical Bayes scaling of Gaussian priors in the white noise model
• Lower bounds for posterior rates with Gaussian process priors
• Bayesian posterior contraction rates for linear severely ill-posed inverse problems
• Bayesian linear inverse problems in regularity scales
• Minimax rates for statistical inverse problems under general source conditions
• Posterior contraction rates for the Bayesian approach to linear ill-posed inverse problems
• The Mathematics of Computerized Tomography
• Posterior consistency and convergence rates for Bayesian inversion with hypoelliptic operators
• Bayesian Optimal Adaptive Estimation Using a Sieve Prior
• Interpolation in variable Hilbert scales with application to inverse problems
• Mathematical Foundations of Infinite-Dimensional Statistical Models
• Tikhonov Regularization for Finitely and Infinitely Smoothing Operators
• Geometry of linear ill-posed problems in variable Hilbert scales
• Discretization strategy for linear ill-posed problems in variable Hilbert scales
• Posterior Contraction in Bayesian Inverse Problems Under Gaussian Priors
• Tikhonov regularization with oversmoothing penalty for non-linear ill-posed problems in Hilbert scales
• Bayesian Recovery of the Initial Condition for the Heat Equation
• Consistency of Bayesian inference with Gaussian process priors in an elliptic inverse problem
• Bayesian inverse problems with non-commuting operators
• Regularization by projection: Approximation theoretic aspects and distance functions
• Regularization by projection in variable Hilbert scales
• How general are general source conditions?

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