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A Stochastic Collocation Approach To Bayesian Inference In Inverse Problems, Youssef Marzouk, Dongbin Xiu

PRISM: NNSA Center for Prediction of Reliability, Integrity and Survivability of Microsystems

We present an efficient numerical strategy for the Bayesian solution of inverse problems. Stochastic collocation methods, based on generalized polynomial chaos (gPC), are used to construct a polynomial approximation of the forward solution over the support of the prior distribution. This approximation then defines a surrogate posterior probability density that can be evaluated repeatedly at minimal computational cost. The ability to simulate a large number of samples from the posterior distribution results in very accurate estimates of the inverse solution and its associated uncertainty. Combined with high accuracy of the gPC-based forward solver, the new algorithm can provide great efficiency …