Parallel Local Approximation MCMC for Expensive Models
Name
16m1084080.pdf
Size
4.88 MB
Format
Adobe PDF
Checksum (MD5)
b5e96e98e0a3ba1d1d7e3d329bccb9a7
Author(s)
Conrad, Patrick Raymond
Davis, Andrew Donaldson
Marzouk, Youssef M
Pillai, Natesh S
Smith, Aaron Robin
Date Issued
March 2018
Journal
SIAM/ASA Journal on Uncertainty Quantification
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Citation
Conrad, Patrick R., Andrew D. Davis, Youssef M. Marzouk, Natesh S. Pillai, and Aaron Smith. “Parallel Local Approximation MCMC for Expensive Models.” SIAM/ASA Journal on Uncertainty Quantification 6, no. 1 (January 2018): 339–373.
Version
Final published version
Abstract
Performing Bayesian inference via Markov chain Monte Carlo (MCMC) can be exceedingly expensive when posterior evaluations invoke the evaluation of a computationally expensive model, such as a system of PDEs. In recent work [J. Amer. Statist. Assoc., 111 (2016), pp. 1591-1607] we described a framework for constructing and refining local approximations of such models during an MCMC simulation. These posterior-adapted approximations harness regularity of the model to reduce the computational cost of inference while preserving asymptotic exactness of the Markov chain. Here we describe two extensions of that work. First, we prove that samplers running in parallel can collaboratively construct a shared posterior approximation while ensuring ergodicity of each associated chain, providing a novel opportunity for exploiting parallel computation in MCMC. Second, focusing on the Metropolis-adjusted Langevin algorithm, we describe how a proposal distribution can successfully employ gradients and other relevant information extracted from the approximation. We investigate the practical performance of our approach using two challenging inference problems, the first in subsurface hydrology and the second in glaciology. Using local approximations constructed via parallel chains, we successfully reduce the run time needed to characterize the posterior distributions in these problems from days to hours and from months to days, respectively, dramatically improving the tractability of Bayesian inference.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Massachusetts Institute of Technology. Department of Mechanical Engineering
Massachusetts Institute of Technology. Institute for Data, Systems, and Society
Massachusetts Institute of Technology. Computation for Design and Optimization Program
MIT Kavli Institute for Astrophysics and Space Research
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1137/16M1084080
