SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Invited Talk

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Gibbs Sampling for Hierarchical Bayesian Inverse Problems

A. Stuart, S. Agapiou, J. Bardsley and O. Papaspiliopoulos

Abstract
I will describe properties of a Gibbs sampler applied to a hierarchical Bayesian formulation of the linear inverse problem. Emphasis will be placed on the insight obtained from formulation of the problem in an infinite dimensional setting and this insight will be used to study convergence properties of Gibbs sampler, based on a splitting into the unknown functions and the hyper-paremeters, as the computational mesh is refined. Posterior consistency properties will also be exhibited, in the small noise limit.

Organized by         Universidad de Valladolid     IMUVA