Bayesian inference with optimal maps
Author(s)
El Moselhy, Tarek A.; Marzouk, Youssef M.
DownloadMarzouk_Bayesian inference.pdf (6.536Mb)
PUBLISHER_CC
Publisher with Creative Commons License
Creative Commons Attribution
Terms of use
Metadata
Show full item recordAbstract
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.
Date issued
2012-08Department
Massachusetts Institute of Technology. Department of Aeronautics and AstronauticsJournal
Journal of Computational Physics
Publisher
Elsevier
Citation
El Moselhy, Tarek A., and Youssef M. Marzouk. “Bayesian Inference with Optimal Maps.” Journal of Computational Physics 231, no. 23 (October 2012): 7815–7850.
Version: Author's final manuscript
ISSN
00219991
1090-2716