Sequential Designs Based on Bayesian Uncertainty Quantification in Sparse Representation Surrogate Modeling
Abstract
A numerical method, called OBSM, was recently proposed which employs overcomplete basis functions to achieve sparse representations. While the method can handle non-stationary response without the need of inverting large covariance matrices, it lacks the capability to quantify uncertainty in predictions. We address this issue by proposing a Bayesian approach which first imposes a normal prior on the large space of linear coefficients, then applies the MCMC algorithm to generate posterior samples for predictions. From these samples, Bayesian credible intervals can then be obtained to assess prediction uncertainty. A key application for the proposed method is the efficient construction of sequential designs. Several sequential design procedures with different infill criteria are proposed based on the generated posterior samples. As a result, numerical studies show that the proposed schemes are capable of solving problems of positive point identification, optimization, and surrogate fitting.
- Authors:
-
- National Cheng Kung Univ. (Taiwan)
- National Taiwan Univ. (Taiwan)
- Georgia Inst. of Technology, Atlanta, GA (United States)
- Publication Date:
- Research Org.:
- Georgia Institute of Technology, Atlanta, GA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
- OSTI Identifier:
- 1405180
- Report Number(s):
- DOE-GT-0010548-6
Journal ID: ISSN 0040-1706; FG02-13ER26159
- Grant/Contract Number:
- SC0010548
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Technometrics
- Additional Journal Information:
- Journal Volume: 59; Journal Issue: 2; Journal ID: ISSN 0040-1706
- Publisher:
- Taylor & Francis
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; Credible interval; Overcomplete bases surrogates method; Posterior sample; Stochastic search variable selection
Citation Formats
Chen, Ray -Bing, Wang, Weichung, and Jeff Wu, C. F. Sequential Designs Based on Bayesian Uncertainty Quantification in Sparse Representation Surrogate Modeling. United States: N. p., 2017.
Web. doi:10.1080/00401706.2016.1172027.
Chen, Ray -Bing, Wang, Weichung, & Jeff Wu, C. F. Sequential Designs Based on Bayesian Uncertainty Quantification in Sparse Representation Surrogate Modeling. United States. https://doi.org/10.1080/00401706.2016.1172027
Chen, Ray -Bing, Wang, Weichung, and Jeff Wu, C. F. Wed .
"Sequential Designs Based on Bayesian Uncertainty Quantification in Sparse Representation Surrogate Modeling". United States. https://doi.org/10.1080/00401706.2016.1172027. https://www.osti.gov/servlets/purl/1405180.
@article{osti_1405180,
title = {Sequential Designs Based on Bayesian Uncertainty Quantification in Sparse Representation Surrogate Modeling},
author = {Chen, Ray -Bing and Wang, Weichung and Jeff Wu, C. F.},
abstractNote = {A numerical method, called OBSM, was recently proposed which employs overcomplete basis functions to achieve sparse representations. While the method can handle non-stationary response without the need of inverting large covariance matrices, it lacks the capability to quantify uncertainty in predictions. We address this issue by proposing a Bayesian approach which first imposes a normal prior on the large space of linear coefficients, then applies the MCMC algorithm to generate posterior samples for predictions. From these samples, Bayesian credible intervals can then be obtained to assess prediction uncertainty. A key application for the proposed method is the efficient construction of sequential designs. Several sequential design procedures with different infill criteria are proposed based on the generated posterior samples. As a result, numerical studies show that the proposed schemes are capable of solving problems of positive point identification, optimization, and surrogate fitting.},
doi = {10.1080/00401706.2016.1172027},
journal = {Technometrics},
number = 2,
volume = 59,
place = {United States},
year = {Wed Apr 12 00:00:00 EDT 2017},
month = {Wed Apr 12 00:00:00 EDT 2017}
}
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