B1631
Title: Exploiting independence in Gaussian importance sampling for Bayesian inverse problems
Authors: Stefan Heyder - TU Ilmenau (Germany) [presenting]
Abstract: In Bayesian inverse problems with Gaussian priors but non-Gaussian observations, one is interested in the properties of the posterior distribution. Instead of obtaining correlated samples from this target via MCMC methods, importance sampling suggests using independent samples from a tractable distribution close to the posterior and reweighting samples accordingly. The choice of a good proposal is crucial to reap the benefits of importance sampling, especially in higher dimensions. The cross-entropy method focuses on minimizing the Kullback-Leibler divergence between the posterior and a Gaussian proposal. However, accounting for the dependency structure in the posterior requires a quadratic number of parameters in the dimension of the problem. It is shown that exploiting the structure of the inverse problem, in particular conditional independence, can lead to more efficient Gaussian proposals, requiring only a linear number of parameters while still accounting for the dependency structure of the posterior.
