Regularized Posteriors in Linear Ill-Posed Inverse Problems

DOI10.1111/j.1467-9469.2011.00784.xzbMath1246.62039OpenAlexW1573629697MaRDI QIDQ2911714

Anna Simoni, Jean-Pierre Florens

Publication date: 1 September 2012

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

Full work available at URL: https://doi.org/10.1111/j.1467-9469.2011.00784.x

zbMATH Keywords

Tikhonov regularizationfunctional datameasurable linear transformationsposterior consistencyGaussian process priors

Mathematics Subject Classification ID

Point estimation (62F10) Bayesian inference (62F15) Monte Carlo methods (65C05) Applications of functional analysis in probability theory and statistics (46N30)

Related Items (9)

Bayes procedures for adaptive inference in inverse problems for the white noise model ⋮ Empirical Bayes scaling of Gaussian priors in the white noise model ⋮ Quasi-Bayesian analysis of nonparametric instrumental variables models ⋮ Nonparametric estimation of an instrumental regression: a quasi-Bayesian approach based on regularized posterior ⋮ Fully Bayesian analysis of the relevance vector machine with an extended hierarchical prior structure ⋮ REGULARIZING PRIORS FOR LINEAR INVERSE PROBLEMS ⋮ Editors' introduction ⋮ A fast and calibrated computer model emulator: an empirical Bayes approach ⋮ Oracle-type posterior contraction rates in Bayesian inverse problems

Uses Software

• fda (R)

Cites Work

• Unnamed Item
• Unnamed Item
• Nonparametric estimation of an instrumental regression: a quasi-Bayesian approach based on regularized posterior
• Nonparametric methods for inference in the presence of instrumental variables
• Rates of contraction of posterior distributions based on Gaussian process priors
• A class of Wasserstein metrics for probability distributions
• Gaussian measures in Banach spaces
• Functional data analysis
• Applied functional data analysis. Methods and case studies
• Discretization-invariant Bayesian inversion and Besov space priors
• On infinite-dimensional hierarchical probability models in statistical inverse problems
• Posterior contraction rates for the Bayesian approach to linear ill-posed inverse problems
• Well-posed stochastic extensions of ill-posed linear problems
• REGULARIZING PRIORS FOR LINEAR INVERSE PROBLEMS
• Inverse problems: A Bayesian perspective
• Inverse problems as statistics
• Non‐parametric Bayesian Inference for Integrals with respect to an Unknown Finite Measure
• Convergence Rates for Linear Inverse Problems in the Presence of an Additive Normal Noise
• Linear inverse problems for generalised random variables
• Linear estimators and measurable linear transformations on a Hilbert space
• Nonparametric Instrumental Regression
• Convergence Rates of General Regularization Methods for Statistical Inverse Problems and Applications
• Convergence rate for the Bayesian approach to linear inverse problems
• Semi-Nonparametric IV Estimation of Shape-Invariant Engel Curves
• Functional Modelling and Classification of Longitudinal Data*
• Consistency and rates of convergence of nonlinear Tikhonov regularization with random noise

This page was built for publication: Regularized Posteriors in Linear Ill-Posed Inverse Problems