A Bayesian approach for parameter estimation and prediction using a computationally intensive model
Abstract
Bayesian methods have been successful in quantifying uncertainty in physicsbased problems in parameter estimation and prediction. In these cases, physical measurements y are modeled as the best fit of a physicsbased model $$\eta (\theta )$$, where θ denotes the uncertain, best input setting. Hence the statistical model is of the form $$y=\eta (\theta )+\epsilon ,$$ where $$\epsilon $$ accounts for measurement, and possibly other, error sources. When nonlinearity is present in $$\eta (\cdot )$$, the resulting posterior distribution for the unknown parameters in the Bayesian formulation is typically complex and nonstandard, requiring computationally demanding computational approaches such as Markov chain Monte Carlo (MCMC) to produce multivariate draws from the posterior. Although generally applicable, MCMC requires thousands (or even millions) of evaluations of the physics model $$\eta (\cdot )$$. This requirement is problematic if the model takes hours or days to evaluate. To overcome this computational bottleneck, we present an approach adapted from Bayesian model calibration. This approach combines output from an ensemble of computational model runs with physical measurements, within a statistical formulation, to carry out inference. A key component of this approach is a statistical response surface, or emulator, estimated from the ensemble of model runs. We demonstrate this approach with a case study in estimating parameters for a density functional theory model, using experimental mass/binding energy measurements from a collection of atomic nuclei. Lastly, we also demonstrate how this approach produces uncertainties in predictions for recent mass measurements obtained at Argonne National Laboratory.
 Authors:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Physics Division
 Argonne National Lab. (ANL), Argonne, IL (United States). Mathematics and Computer Science Division
 Publication Date:
 Research Org.:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC21)
 OSTI Identifier:
 1378523
 Alternate Identifier(s):
 OSTI ID: 1407869
 Report Number(s):
 LLNLJRNL737147; LAUR1426925
Journal ID: ISSN 09543899
 Grant/Contract Number:
 AC5207NA27344; AC5206NA25396
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Journal of Physics. G, Nuclear and Particle Physics
 Additional Journal Information:
 Journal Volume: 42; Journal Issue: 3; Journal ID: ISSN 09543899
 Publisher:
 IOP Publishing
 Country of Publication:
 United States
 Language:
 English
 Subject:
 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
Citation Formats
Higdon, Dave, McDonnell, Jordan D., Schunck, Nicolas, Sarich, Jason, and Wild, Stefan M.. A Bayesian approach for parameter estimation and prediction using a computationally intensive model. United States: N. p., 2015.
Web. doi:10.1088/09543899/42/3/034009.
Higdon, Dave, McDonnell, Jordan D., Schunck, Nicolas, Sarich, Jason, & Wild, Stefan M.. A Bayesian approach for parameter estimation and prediction using a computationally intensive model. United States. doi:10.1088/09543899/42/3/034009.
Higdon, Dave, McDonnell, Jordan D., Schunck, Nicolas, Sarich, Jason, and Wild, Stefan M.. 2015.
"A Bayesian approach for parameter estimation and prediction using a computationally intensive model". United States.
doi:10.1088/09543899/42/3/034009. https://www.osti.gov/servlets/purl/1378523.
@article{osti_1378523,
title = {A Bayesian approach for parameter estimation and prediction using a computationally intensive model},
author = {Higdon, Dave and McDonnell, Jordan D. and Schunck, Nicolas and Sarich, Jason and Wild, Stefan M.},
abstractNote = {Bayesian methods have been successful in quantifying uncertainty in physicsbased problems in parameter estimation and prediction. In these cases, physical measurements y are modeled as the best fit of a physicsbased model $\eta (\theta )$, where θ denotes the uncertain, best input setting. Hence the statistical model is of the form $y=\eta (\theta )+\epsilon ,$ where $\epsilon $ accounts for measurement, and possibly other, error sources. When nonlinearity is present in $\eta (\cdot )$, the resulting posterior distribution for the unknown parameters in the Bayesian formulation is typically complex and nonstandard, requiring computationally demanding computational approaches such as Markov chain Monte Carlo (MCMC) to produce multivariate draws from the posterior. Although generally applicable, MCMC requires thousands (or even millions) of evaluations of the physics model $\eta (\cdot )$. This requirement is problematic if the model takes hours or days to evaluate. To overcome this computational bottleneck, we present an approach adapted from Bayesian model calibration. This approach combines output from an ensemble of computational model runs with physical measurements, within a statistical formulation, to carry out inference. A key component of this approach is a statistical response surface, or emulator, estimated from the ensemble of model runs. We demonstrate this approach with a case study in estimating parameters for a density functional theory model, using experimental mass/binding energy measurements from a collection of atomic nuclei. Lastly, we also demonstrate how this approach produces uncertainties in predictions for recent mass measurements obtained at Argonne National Laboratory.},
doi = {10.1088/09543899/42/3/034009},
journal = {Journal of Physics. G, Nuclear and Particle Physics},
number = 3,
volume = 42,
place = {United States},
year = 2015,
month = 2
}
Web of Science

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