Dimension-independent likelihood-informed MCMC

Cui, Tiangang; Law, Kody J. H.; Marzouk, Youssef M.

doi:10.1016/j.jcp.2015.10.008

Title: Dimension-independent likelihood-informed MCMC

Journal Article · Thu Oct 08 00:00:00 EDT 2015 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2015.10.008· OSTI ID:1324173

Cui, Tiangang ^[1]; Law, Kody J. H. ^[2]; Marzouk, Youssef M. ^[1]

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Many Bayesian inference problems require exploring the posterior distribution of highdimensional parameters that represent the discretization of an underlying function. Our work introduces a family of Markov chain Monte Carlo (MCMC) samplers that can adapt to the particular structure of a posterior distribution over functions. There are two distinct lines of research that intersect in the methods we develop here. First, we introduce a general class of operator-weighted proposal distributions that are well defined on function space, such that the performance of the resulting MCMC samplers is independent of the discretization of the function. Second, by exploiting local Hessian information and any associated lowdimensional structure in the change from prior to posterior distributions, we develop an inhomogeneous discretization scheme for the Langevin stochastic differential equation that yields operator-weighted proposals adapted to the non-Gaussian structure of the posterior. The resulting dimension-independent and likelihood-informed (DILI) MCMC samplers may be useful for a large class of high-dimensional problems where the target probability measure has a density with respect to a Gaussian reference measure. Finally, we use two nonlinear inverse problems in order to demonstrate the efficiency of these DILI samplers: an elliptic PDE coefficient inverse problem and path reconstruction in a conditioned diffusion.

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Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC05-00OR22725; SC0009297

OSTI ID:: 1324173

Alternate ID(s):: OSTI ID: 1359277

Journal Information:: Journal of Computational Physics, Vol. 304, Issue C; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 100 works

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Randomized Truncated SVD Levenberg‐Marquardt Approach to Geothermal Natural State and History Matching Bjarkason, Elvar K.; Maclaren, Oliver J.; O'Sullivan, John P. Water Resources Research, Vol. 54, Issue 3 https://doi.org/10.1002/2017wr021870	journal	March 2018
Inverse problems: From regularization to Bayesian inference Calvetti, D.; Somersalo, E. WIREs Computational Statistics, Vol. 10, Issue 3 https://doi.org/10.1002/wics.1427	journal	January 2018
Efficient parameter estimation for a methane hydrate model with active subspaces Teixeira Parente, Mario; Mattis, Steven; Gupta, Shubhangi Computational Geosciences, Vol. 23, Issue 2 https://doi.org/10.1007/s10596-018-9769-x	journal	August 2018
Wavelet-Based Priors Accelerate Maximum-a-Posteriori Optimization in Bayesian Inverse Problems Wacker, Philipp; Knabner, Peter Methodology and Computing in Applied Probability, Vol. 22, Issue 3 https://doi.org/10.1007/s11009-019-09736-2	journal	July 2019
Spatial Localization for Nonlinear Dynamical Stochastic Models for Excitable Media Chen, Nan; Majda, Andrew J.; Tong, Xin T. Chinese Annals of Mathematics, Series B, Vol. 40, Issue 6 https://doi.org/10.1007/s11401-019-0166-0	journal	November 2019
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Bayesian Calibration and Sensitivity Analysis for a Karst Aquifer Model Using Active Subspaces Teixeira Parente, Mario; Bittner, Daniel; Mattis, Steven A. FID GEO https://doi.org/10.23689/fidgeo-4887	text	January 2019
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Spatial localization for nonlinear dynamical stochastic models for excitable media Chen, Nan; Majda, Andrew J.; Tong, Xin T. arXiv https://doi.org/10.48550/arxiv.1901.07318	preprint	January 2019

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