Global Sensitivity Analysis for Statistical Model Parameters

Hart, Joseph L.; Bessac, Julie; Constantinescu, Emil M.

doi:10.1137/17M1161397

Title: Global Sensitivity Analysis for Statistical Model Parameters

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Abstract

Global sensitivity analysis (GSA) is typically used to analyze the influence of uncertain parameters in mathematical models and simulations. In principle, tools from GSA may be extended to analyze the influence of parameters in statistical models. Such analyses may enable reduced or parsimonious modeling and greater predictive capability. Yet, difficulties such as parameter correlation, model stochasticity, multivariate model output, and unknown parameter distributions prohibit a direct application of GSA tools to statistical models. By leveraging a loss function associated with the statistical model, we introduce a novel framework to address these difficulties and enable efficient GSA for statistical model parameters. Theoretical and computational properties are considered and hihglighted on a synthetic example. The framework is applied to a Gaussian process model from the literature, which depends on 95 parameters. Noninfluential parameters are discovered through GSA, and a reduced model with equal or stronger predictive capability is constructed by using only 79 parameters.

Authors:

Hart, Joseph L. ^[1]; Bessac, Julie ^[2];

^[2]

North Carolina State Univ., Raleigh, NC (United States)
Argonne National Lab. (ANL), Argonne, IL (United States)

Publication Date:: Thu Jan 03 00:00:00 EST 2019

Research Org.:: Argonne National Lab. (ANL), Argonne, IL (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); National Science Foundation (NSF)

OSTI Identifier:: 1510482

Grant/Contract Number:: AC02-06CH11357

Resource Type:: Accepted Manuscript

Journal Name:: SIAM/ASA Journal on Uncertainty Quantification

Additional Journal Information:: Journal Volume: 7; Journal Issue: 1; Journal ID: ISSN 2166-2525

Publisher:: SIAM

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; Correlated parameters; Dimension reduction; Global sensitivity analysis; Markov Chain Monte Carlo

Citation Formats


                    Hart, Joseph L., Bessac, Julie, and Constantinescu, Emil M. Global Sensitivity Analysis for Statistical Model Parameters.  United States: N. p., 2019. 
Web.  doi:10.1137/17M1161397.

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                    Hart, Joseph L., Bessac, Julie, & Constantinescu, Emil M. Global Sensitivity Analysis for Statistical Model Parameters.  United States.  https://doi.org/10.1137/17M1161397

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                    Hart, Joseph L., Bessac, Julie, and Constantinescu, Emil M. Thu .  
"Global Sensitivity Analysis for Statistical Model Parameters".  United States.  https://doi.org/10.1137/17M1161397.  https://www.osti.gov/servlets/purl/1510482.

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@article{osti_1510482,

  title        = {Global Sensitivity Analysis for Statistical Model Parameters},

  author       = {Hart, Joseph L. and Bessac, Julie and Constantinescu, Emil M.},

  abstractNote = {Global sensitivity analysis (GSA) is typically used to analyze the influence of uncertain parameters in mathematical models and simulations. In principle, tools from GSA may be extended to analyze the influence of parameters in statistical models. Such analyses may enable reduced or parsimonious modeling and greater predictive capability. Yet, difficulties such as parameter correlation, model stochasticity, multivariate model output, and unknown parameter distributions prohibit a direct application of GSA tools to statistical models. By leveraging a loss function associated with the statistical model, we introduce a novel framework to address these difficulties and enable efficient GSA for statistical model parameters. Theoretical and computational properties are considered and hihglighted on a synthetic example. The framework is applied to a Gaussian process model from the literature, which depends on 95 parameters. Noninfluential parameters are discovered through GSA, and a reduced model with equal or stronger predictive capability is constructed by using only 79 parameters.},

  doi          = {10.1137/17M1161397},

  journal      = {SIAM/ASA Journal on Uncertainty Quantification},

  number       = 1,

  volume       = 7,

  place        = {United States},

  year         = {Thu Jan 03 00:00:00 EST 2019},

  month        = {Thu Jan 03 00:00:00 EST 2019}

}

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