Published in
Proceedings of the 1st International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECOMP 2015)
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Variational Reformulation of Bayesian Inverse Problems
,
Ilias Bilionis,
Ioannis Katsounaros,
Nicholas Zabaras
Abstract
The classical approach to inverse problems is based on the optimization of a misfit function. Despite its computational appeal, such an approach suffers from many shortcomings, e.g., non-uniqueness of solutions, modeling prior knowledge, etc. The Bayesian formalism to inverse problems avoids most of the difficulties encountered by the optimization approach, albeit at an increased computational cost. In this work, we use information theoretic arguments to cast the Bayesian inference problem in terms of an optimization problem. The resulting scheme combines the theoretical soundness of fully Bayesian inference with the computational efficiency of a simple optimization.