Bayesian inference with optimal maps

被引:151
作者
El Moselhy, Tarek A. [1 ]
Marzouk, Youssef M. [1 ]
机构
[1] MIT, Cambridge, MA 02139 USA
关键词
Bayesian inference; Optimal transport; Measure-preserving maps; Inverse problems; Polynomial chaos; Numerical optimization; POLYNOMIAL CHAOS; INVERSE PROBLEMS; CHAIN; APPROXIMATION; SIMULATIONS; UNCERTAINTY; COARSE;
D O I
10.1016/j.jcp.2012.07.022
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
We present a new approach to Bayesian inference that entirely avoids Markov chain simulation, by constructing a map that pushes forward the prior measure to the posterior measure. Existence and uniqueness of a suitable measure-preserving map is established by formulating the problem in the context of optimal transport theory. We discuss various means of explicitly parameterizing the map and computing it efficiently through solution of an optimization problem, exploiting gradient information from the forward model when possible. The resulting algorithm overcomes many of the computational bottlenecks associated with Markov chain Monte Carlo. Advantages of a map-based representation of the posterior include analytical expressions for posterior moments and the ability to generate arbitrary numbers of independent posterior samples without additional likelihood evaluations or forward solves. The optimization approach also provides clear convergence criteria for posterior approximation and facilitates model selection through automatic evaluation of the marginal likelihood. We demonstrate the accuracy and efficiency of the approach on nonlinear inverse problems of varying dimension, involving the inference of parameters appearing in ordinary and partial differential equations. (C) 2012 Elsevier Inc. All rights reserved.
引用
收藏
页码:7815 / 7850
页数:36
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