MIT Libraries logoDSpace@MIT

MIT
View Item 
  • DSpace@MIT Home
  • MIT Open Access Articles
  • MIT Open Access Articles
  • View Item
  • DSpace@MIT Home
  • MIT Open Access Articles
  • MIT Open Access Articles
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Bayesian inference with optimal maps

Author(s)
El Moselhy, Tarek A.; Marzouk, Youssef M.
Thumbnail
DownloadMarzouk_Bayesian inference.pdf (6.536Mb)
PUBLISHER_CC

Publisher with Creative Commons License

Creative Commons Attribution

Terms of use
Creative Commons Attribution-Noncommercial-NoDerivatives http://creativecommons.org/licenses/by-nc-nd/4.0/
Metadata
Show full item record
Abstract
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
2012-08
URI
http://hdl.handle.net/1721.1/99466
Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Journal
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

Collections
  • MIT Open Access Articles

Browse

All of DSpaceCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

My Account

Login

Statistics

OA StatisticsStatistics by CountryStatistics by Department
MIT Libraries
PrivacyPermissionsAccessibilityContact us
MIT
Content created by the MIT Libraries, CC BY-NC unless otherwise noted. Notify us about copyright concerns.