Posterior contraction rates for the Bayesian approach to linear ill-posed inverse problems
Journal article, 2013

We consider a Bayesian nonparametric approach to a family of linear inverse problems in a separable Hilbert space setting with Gaussian noise. We assume Gaussian priors, which are conjugate to the model, and present a method of identifying the posterior using its precision operator. Working with the unbounded precision operator enables us to use partial differential equations (PDE) methodology to obtain rates of contraction of the posterior distribution to a Dirac measure centered on the true solution. Our methods assume a relatively weak relation between the prior covariance, noise covariance and forward operator, allowing for a wide range of applications.

Posterior contraction

Gaussian prior

Inverse problems

Posterior distribution

Posterior consistency

Author

Sergios Agapiou

The University of Warwick

Stig Larsson

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Andrew M. Stuart

The University of Warwick

Stochastic Processes and their Applications

0304-4149 (ISSN)

Vol. 123 10 3828-3860

Roots

Basic sciences

Subject Categories

Probability Theory and Statistics

DOI

10.1016/j.spa.2013.05.001

More information

Created

10/8/2017