An Approximate Bayesian Approach for Uncertainty Quantification in EIT

Matthias Gehre^*

We present a fast approximate inference method based on expectation propagation for exploring Bayesian formulations for nonlinear inverse problems. The basic idea of the method and its properties will be discussed. It can efficiently deliver the posterior mean and covariance, thereby providing reliable point estimates with quantified uncertainties. Numerical results from experimental data for one typical nonlinear inverse problem, electrical impedance tomography (EIT) with the complete electrode model, will be presented, and compared with those by Markov chain Monte Carlo.

Mathematics Subject Classification: 65N21 65C50

Keywords: Expectation propagation, nonlinear inverse problem, uncertainty quantification, sparsity constraints, electrical impedance tomography, bayesian inference

Minisymposion: Dual Methods for Approaching Inverse Problems