Designing truncated priors for direct and inverse Bayesian problems
arXiv:2105.10254 · doi:10.1214/21-EJS1966
Abstract
The Bayesian approach to inverse problems with functional unknowns, has received significant attention in recent years. An important component of the developing theory is the study of the asymptotic performance of the posterior distribution in the frequentist setting. The present paper contributes to the area of Bayesian inverse problems by formulating a posterior contraction theory for linear inverse problems, with truncated Gaussian series priors, and under general smoothness assumptions. Emphasis is on the intrinsic role of the truncation point both for the direct as well as for the inverse problem, which are related through the modulus of continuity as this was recently highlighted by Knapik and Salomond (2018).
References in corpus (13)
- Rates of contraction of posterior distributions based on Gaussian process priors
- Convergence rates of posterior distributions for noniid observations
- Bayesian inverse problems with Gaussian priors
- Posterior Contraction Rates for the Bayesian Approach to Linear Ill-Posed Inverse Problems
- Bayesian inverse problems with non-conjugate priors
- Lower bounds for posterior rates with Gaussian process priors
- Bayesian recovery of the initial condition for the heat equation
- Tikhonov regularization with oversmoothing penalty for non-linear ill-posed problems in Hilbert scales
- Bayesian optimal adaptive estimation using a sieve prior
- Bayesian Posterior Contraction Rates for Linear Severely Ill-posed Inverse Problems
- Posterior consistency and convergence rates for Bayesian inversion with hypoelliptic operators
- Bayesian inverse problems with non-commuting operators
- Bayesian linear inverse problems in regularity scales