## This content will become publicly available on January 3, 2020

# Global Sensitivity Analysis for Statistical Model Parameters

## 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:

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

- Publication Date:

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

- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21); 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:
- 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.
```

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

```
Hart, Joseph L., Bessac, Julie, and Constantinescu, Emil M. Thu .
"Global Sensitivity Analysis for Statistical Model Parameters". United States. doi:10.1137/17M1161397.
```

```
@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 = {2019},

month = {1}

}