A new framework for comprehensive, robust, and efficient global sensitivity analysis

1. Theory

Saman Razavi, Hoshin Vijai Gupta

Research output: Contribution to journalArticle

31 Citations (Scopus)

Abstract

Computer simulation models are continually growing in complexity with increasingly more factors to be identified. Sensitivity Analysis (SA) provides an essential means for understanding the role and importance of these factors in producing model responses. However, conventional approaches to SA suffer from (1) an ambiguous characterization of sensitivity, and (2) poor computational efficiency, particularly as the problem dimension grows. Here, we present a new and general sensitivity analysis framework (called VARS), based on an analogy to "variogram analysis," that provides an intuitive and comprehensive characterization of sensitivity across the full spectrum of scales in the factor space. We prove, theoretically, that Morris (derivative-based) and Sobol (variance-based) methods and their extensions are special cases of VARS, and that their SA indices can be computed as by-products of the VARS framework. Synthetic functions that resemble actual model response surfaces are used to illustrate the concepts, and show VARS to be as much as two orders of magnitude more computationally efficient than the state-of-the-art Sobol approach. In a companion paper, we propose a practical implementation strategy, and demonstrate the effectiveness, efficiency, and reliability (robustness) of the VARS framework on real-data case studies.

Original languageEnglish (US)
JournalWater Resources Research
DOIs
StateAccepted/In press - 2016

Fingerprint

sensitivity analysis
variogram
computer simulation

Keywords

  • Bootstrapping
  • Computational efficiency
  • Covariogram
  • Dynamical models
  • Model performance
  • Morris
  • Sampling
  • Scale
  • Sensitivity analysis
  • Sobol
  • Variogram

ASJC Scopus subject areas

  • Water Science and Technology

Cite this

@article{e7ab66c69f024fc5a64f271dd63f5148,
title = "A new framework for comprehensive, robust, and efficient global sensitivity analysis: 1. Theory",
abstract = "Computer simulation models are continually growing in complexity with increasingly more factors to be identified. Sensitivity Analysis (SA) provides an essential means for understanding the role and importance of these factors in producing model responses. However, conventional approaches to SA suffer from (1) an ambiguous characterization of sensitivity, and (2) poor computational efficiency, particularly as the problem dimension grows. Here, we present a new and general sensitivity analysis framework (called VARS), based on an analogy to {"}variogram analysis,{"} that provides an intuitive and comprehensive characterization of sensitivity across the full spectrum of scales in the factor space. We prove, theoretically, that Morris (derivative-based) and Sobol (variance-based) methods and their extensions are special cases of VARS, and that their SA indices can be computed as by-products of the VARS framework. Synthetic functions that resemble actual model response surfaces are used to illustrate the concepts, and show VARS to be as much as two orders of magnitude more computationally efficient than the state-of-the-art Sobol approach. In a companion paper, we propose a practical implementation strategy, and demonstrate the effectiveness, efficiency, and reliability (robustness) of the VARS framework on real-data case studies.",
keywords = "Bootstrapping, Computational efficiency, Covariogram, Dynamical models, Model performance, Morris, Sampling, Scale, Sensitivity analysis, Sobol, Variogram",
author = "Saman Razavi and Gupta, {Hoshin Vijai}",
year = "2016",
doi = "10.1002/2015WR017558",
language = "English (US)",
journal = "Water Resources Research",
issn = "0043-1397",
publisher = "American Geophysical Union",

}

TY - JOUR

T1 - A new framework for comprehensive, robust, and efficient global sensitivity analysis

T2 - 1. Theory

AU - Razavi, Saman

AU - Gupta, Hoshin Vijai

PY - 2016

Y1 - 2016

N2 - Computer simulation models are continually growing in complexity with increasingly more factors to be identified. Sensitivity Analysis (SA) provides an essential means for understanding the role and importance of these factors in producing model responses. However, conventional approaches to SA suffer from (1) an ambiguous characterization of sensitivity, and (2) poor computational efficiency, particularly as the problem dimension grows. Here, we present a new and general sensitivity analysis framework (called VARS), based on an analogy to "variogram analysis," that provides an intuitive and comprehensive characterization of sensitivity across the full spectrum of scales in the factor space. We prove, theoretically, that Morris (derivative-based) and Sobol (variance-based) methods and their extensions are special cases of VARS, and that their SA indices can be computed as by-products of the VARS framework. Synthetic functions that resemble actual model response surfaces are used to illustrate the concepts, and show VARS to be as much as two orders of magnitude more computationally efficient than the state-of-the-art Sobol approach. In a companion paper, we propose a practical implementation strategy, and demonstrate the effectiveness, efficiency, and reliability (robustness) of the VARS framework on real-data case studies.

AB - Computer simulation models are continually growing in complexity with increasingly more factors to be identified. Sensitivity Analysis (SA) provides an essential means for understanding the role and importance of these factors in producing model responses. However, conventional approaches to SA suffer from (1) an ambiguous characterization of sensitivity, and (2) poor computational efficiency, particularly as the problem dimension grows. Here, we present a new and general sensitivity analysis framework (called VARS), based on an analogy to "variogram analysis," that provides an intuitive and comprehensive characterization of sensitivity across the full spectrum of scales in the factor space. We prove, theoretically, that Morris (derivative-based) and Sobol (variance-based) methods and their extensions are special cases of VARS, and that their SA indices can be computed as by-products of the VARS framework. Synthetic functions that resemble actual model response surfaces are used to illustrate the concepts, and show VARS to be as much as two orders of magnitude more computationally efficient than the state-of-the-art Sobol approach. In a companion paper, we propose a practical implementation strategy, and demonstrate the effectiveness, efficiency, and reliability (robustness) of the VARS framework on real-data case studies.

KW - Bootstrapping

KW - Computational efficiency

KW - Covariogram

KW - Dynamical models

KW - Model performance

KW - Morris

KW - Sampling

KW - Scale

KW - Sensitivity analysis

KW - Sobol

KW - Variogram

UR - http://www.scopus.com/inward/record.url?scp=84955584890&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84955584890&partnerID=8YFLogxK

U2 - 10.1002/2015WR017558

DO - 10.1002/2015WR017558

M3 - Article

JO - Water Resources Research

JF - Water Resources Research

SN - 0043-1397

ER -