Variational Bayesian Formulations for High-Dimensional Inverse Problems

The present paper advocates a Variational Bayesian (VB) approach for approximating the posterior density in stochastic inverse problems. In contrast to sampling techniques (e.g. MCMC, SMC), VB requires much fewer forward evaluations. Furthermore it enables learning of a suitable lower-dimensional subspace where most of the posterior probability lies, and reducing dramatically the number of unknowns. We demonstrate the accuracy and efficiency of the proposed strategy in nonlinear problems and non-Gaussian posteriors in view of biomedical applications.     «

The present paper advocates a Variational Bayesian (VB) approach for approximating the posterior density in stochastic inverse problems. In contrast to sampling techniques (e.g. MCMC, SMC), VB requires much fewer forward evaluations. Furthermore it enables learning of a suitable lower-dimensional subspace where most of the posterior probability lies, and reducing dramatically the number of unknowns. We demonstrate the accuracy and efficiency of the proposed strategy in nonlinear problems and non...     »