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Title: An adaptive importance sampling algorithm for Bayesian inversion with multimodal distributions

Abstract

Parametric uncertainties are encountered in the simulations of many physical systems, and may be reduced by an inverse modeling procedure that calibrates the simulation results to observations on the real system being simulated. Following Bayes’ rule, a general approach for inverse modeling problems is to sample from the posterior distribution of the uncertain model parameters given the observations. However, the large number of repetitive forward simulations required in the sampling process could pose a prohibitive computational burden. This difficulty is particularly challenging when the posterior is multimodal. We present in this paper an adaptive importance sampling algorithm to tackle these challenges. Two essential ingredients of the algorithm are: 1) a Gaussian mixture (GM) model adaptively constructed as the proposal distribution to approximate the possibly multimodal target posterior, and 2) a mixture of polynomial chaos (PC) expansions, built according to the GM proposal, as a surrogate model to alleviate the computational burden caused by computational-demanding forward model evaluations. In three illustrative examples, the proposed adaptive importance sampling algorithm demonstrates its capabilities of automatically finding a GM proposal with an appropriate number of modes for the specific problem under study, and obtaining a sample accurately and efficiently representing the posterior with limitedmore » number of forward simulations.« less

Authors:
 [1];  [2]
+ Show Author Affiliations
  1. Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
  2. Purdue University, West Lafayette, IN (United States)
Publication Date:
Research Org.:
Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
OSTI Identifier:
1182897
Alternate Identifier(s):
OSTI ID: 1367756
Report Number(s):
PNNL-SA-105408
Journal ID: ISSN 0021-9991; KJ0401000
Grant/Contract Number:  
DMS-1115887; AC05-76RL01830
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 294; Journal Issue: C; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; inverse modeling, uncertainty reduction, adaptive sampling, Gaussian mixture, mixture of polynomial chaos expansions

Citation Formats

Li, Weixuan, and Lin, Guang. An adaptive importance sampling algorithm for Bayesian inversion with multimodal distributions. United States: N. p., 2015. Web. doi:10.1016/j.jcp.2015.03.047.
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Li, Weixuan, & Lin, Guang. An adaptive importance sampling algorithm for Bayesian inversion with multimodal distributions. United States. https://doi.org/10.1016/j.jcp.2015.03.047
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Li, Weixuan, and Lin, Guang. Sat . "An adaptive importance sampling algorithm for Bayesian inversion with multimodal distributions". United States. https://doi.org/10.1016/j.jcp.2015.03.047. https://www.osti.gov/servlets/purl/1182897.
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@article{osti_1182897,
title = {An adaptive importance sampling algorithm for Bayesian inversion with multimodal distributions},
author = {Li, Weixuan and Lin, Guang},
abstractNote = {Parametric uncertainties are encountered in the simulations of many physical systems, and may be reduced by an inverse modeling procedure that calibrates the simulation results to observations on the real system being simulated. Following Bayes’ rule, a general approach for inverse modeling problems is to sample from the posterior distribution of the uncertain model parameters given the observations. However, the large number of repetitive forward simulations required in the sampling process could pose a prohibitive computational burden. This difficulty is particularly challenging when the posterior is multimodal. We present in this paper an adaptive importance sampling algorithm to tackle these challenges. Two essential ingredients of the algorithm are: 1) a Gaussian mixture (GM) model adaptively constructed as the proposal distribution to approximate the possibly multimodal target posterior, and 2) a mixture of polynomial chaos (PC) expansions, built according to the GM proposal, as a surrogate model to alleviate the computational burden caused by computational-demanding forward model evaluations. In three illustrative examples, the proposed adaptive importance sampling algorithm demonstrates its capabilities of automatically finding a GM proposal with an appropriate number of modes for the specific problem under study, and obtaining a sample accurately and efficiently representing the posterior with limited number of forward simulations.},
doi = {10.1016/j.jcp.2015.03.047},
journal = {Journal of Computational Physics},
number = C,
volume = 294,
place = {United States},
year = {Sat Mar 21 00:00:00 EDT 2015},
month = {Sat Mar 21 00:00:00 EDT 2015}
}
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Journal Article:
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Publisher's Version of Record
https://doi.org/10.1016/j.jcp.2015.03.047
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Works referenced in this record:

Identification of multi-modal random variables through mixtures of polynomial chaos expansions
journal, December 2010

Modeling uncertainty in flow simulations via generalized polynomial chaos
journal, May 2003

Inverse problems: A Bayesian perspective
journal, May 2010

Adaptive independence samplers
journal, May 2008

  • Keith, Jonathan M.; Kroese, Dirk P.; Sofronov, George Y.
  • Statistics and Computing, Vol. 18, Issue 4
  • DOI: 10.1007/s11222-008-9070-2

Adaptive importance sampling in general mixture classes
journal, April 2008

Adaptive Construction of Surrogates for the Bayesian Solution of Inverse Problems
journal, January 2014

  • Li, Jinglai; Marzouk, Youssef M.
  • SIAM Journal on Scientific Computing, Vol. 36, Issue 3
  • DOI: 10.1137/130938189

Bayesian calibration of computer models
journal, August 2001

  • Kennedy, Marc C.; O'Hagan, Anthony
  • Journal of the Royal Statistical Society: Series B (Statistical Methodology), Vol. 63, Issue 3
  • DOI: 10.1111/1467-9868.00294

Combining Field Data and Computer Simulations for Calibration and Prediction
journal, January 2004

  • Higdon, Dave; Kennedy, Marc; Cavendish, James C.
  • SIAM Journal on Scientific Computing, Vol. 26, Issue 2
  • DOI: 10.1137/S1064827503426693

Bayesian Calibration and Uncertainty Analysis for Computationally Expensive Models Using Optimization and Radial Basis Function Approximation
journal, June 2008

  • Bliznyuk, Nikolay; Ruppert, David; Shoemaker, Christine
  • Journal of Computational and Graphical Statistics, Vol. 17, Issue 2
  • DOI: 10.1198/106186008X320681

Multiple-pattern parameter identification and uncertainty analysis approach for water quality modeling
journal, March 2009

The Homogeneous Chaos
journal, October 1938

  • Wiener, Norbert
  • American Journal of Mathematics, Vol. 60, Issue 4
  • DOI: 10.2307/2371268

Stochastic analysis of unsaturated flow with probabilistic collocation method: PCM MODELING OF UNSATURATED FLOW
journal, August 2009

  • Li, Weixuan; Lu, Zhiming; Zhang, Dongxiao
  • Water Resources Research, Vol. 45, Issue 8
  • DOI: 10.1029/2008WR007530

Stochastic spectral methods for efficient Bayesian solution of inverse problems
journal, June 2007

  • Marzouk, Youssef M.; Najm, Habib N.; Rahn, Larry A.
  • Journal of Computational Physics, Vol. 224, Issue 2
  • DOI: 10.1016/j.jcp.2006.10.010

An adaptive ANOVA-based PCKF for high-dimensional nonlinear inverse modeling
journal, February 2014

Identification of multi-modal random variables through mixtures of polynomial chaos expansions
journal, December 2010

An adaptive multi-element generalized polynomial chaos method for stochastic differential equations
journal, November 2005

On the Convergence Properties of the EM Algorithm
journal, March 1983

Errors in History Matching
journal, September 2004

  • Tavassoli, Z.; Carter, Jonathan N.; King, Peter R.
  • SPE Journal, Vol. 9, Issue 03
  • DOI: 10.2118/86883-PA

Our calibrated model has poor predictive value: An example from the petroleum industry
journal, October 2006

  • Carter, J. N.; Ballester, P. J.; Tavassoli, Z.
  • Reliability Engineering & System Safety, Vol. 91, Issue 10-11
  • DOI: 10.1016/j.ress.2005.11.033

Uncertainty quantification for porous media flows
journal, September 2006

  • Christie, Mike; Demyanov, Vasily; Erbas, Demet
  • Journal of Computational Physics, Vol. 217, Issue 1
  • DOI: 10.1016/j.jcp.2006.01.026
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