A Stochastic Collocation Approach to Bayesian Inference in Inverse Problems

作     者：Youssef Marzouk Dongbin Xiu 

作者机构：Department of Aeronautics&AstronauticsMassachusetts Institute of TechnologyCambridgeMA 02139USA Department of MathematicsPurdue UniversityWest LafayetteIN 47907USA 

出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)

年 卷 期：2009年第6卷第9期

页      面：826-847页

核心收录：

学科分类：07[理学] 0704[理学-天文学] 0701[理学-数学] 0702[理学-物理学] 070101[理学-基础数学] 

基　　金：The work of Y.Marzouk is supported in part by the DOE Office of Advanced Scientific Computing Research(ASCR) by Sandia Corporation(a wholly owned subsidiary of Lockheed Martin Corporation)as operator of Sandia National Laboratories under US Department of Energy contract number DE-AC04-94AL85000 The work of D.Xiu is supported in part by AFOSR FA9550-08-1-0353,NSF CAREER Award DMS-0645035 the DOE/NNSA PSAAP center at Purdue(PRISM)under contract number DE-FC52-08NA28617 

主　　题：Inverse problems Bayesian inference stochastic collocation generalized polynomial chaos uncertainty quantification 

摘      要：We present an efficient numerical strategy for the Bayesian solution of inverse *** 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 *** approximation then defines a surrogate posterior probability density that can be evaluated repeatedly at minimal computational *** ability to simulate a large number of samples from the posterior distribution results in very accurate estimates of the inverse solution and its associated *** with high accuracy of the gPC-based forward solver,the new algorithm can provide great efficiency in practical applications.A rigorous error analysis of the algorithm is conducted,where we establish convergence of the approximate posterior to the true posterior and obtain an estimate of the convergence *** is proved that fast(exponential)convergence of the gPC forward solution yields similarly fast(exponential)convergence of the *** numerical strategy and the predicted convergence rates are then demonstrated on nonlinear inverse problems of varying smoothness and dimension.