B0603
Title: Sample free inference for Bayesian inverse problems, a local approximation
Authors: Odd Kolbjornsen - University of Oslo (Norway) [presenting]
Charlotte Semin-Sanchis - Norsk Regnesentral (Norway)
Abstract: Many problems of indirect measurements fit into a framework of inverse problems where the data are linked to a target property through an intermediate property. The intermediate property is essential to explain the physics of the problem, and is dependent on the target variable but can be considered a nuisance parameter in the inference. In x-ray tomography, the data are line integrals of the absorption, whereas the target property is tissue type or density. For seismic data, the interest might be the rock type or the porosity, but the physics is related to intermediate properties such as sound velocity and density. The hierarchical structure of the problem and the multiple levels of uncertainty makes the problem well-suited for a Bayesian formulation. However, the general solution to Bayesian inference through McMC sampling is, in general, too time-consuming for large-scale problems. We present an approximate computation which provides a sampling-free Bayesian inversion based on the principles of expectation propagation. The approach is valid for a large class of inverse problems. Going from a global problem, we build on the likelihood principle to provide an approximate likelihood which is suited for local inference. We show examples from CT images of rock and seismic amplitude inversion.
