Bayesian inference with optimal maps
Name
Marzouk_Bayesian inference.pdf
Size
6.54 MB
Format
Adobe PDF
Checksum (MD5)
5912486118f9ee0615335db0f6f17e7a
Author(s)
El Moselhy, Tarek A.
Marzouk, Youssef M.
Date Issued
August 2012
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
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.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Terms of Use
Creative Commons Attribution-Noncommercial-NoDerivatives
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1016/j.jcp.2012.07.022
