{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/137606"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/137606","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Advances in Sobol' Index Estimation: Metamodeling, Multilevel Monte Carlo Metamodeling, and Nested Simulation Techniques","abstract":"Sobol' indices are widely used in global sensitivity analysis to quantify input variable contributions to output variance in complex computational models. Traditional methods become impractical due to prohibitive computational costs, difficulties managing model stochasticity and multivariate outputs, and experimental design constraints. This dissertation addresses these limitations through advanced techniques based on metamodeling, multilevel Monte Carlo (MLMC) metamodeling, and nested simulation. We develop two joint metamodel-based estimators for Sobol' indices with established asymptotic normality, enabling reliable uncertainty quantification. Our proposed MLMC metamodeling approach for variance function estimation substantially reduces computational complexity, yielding competitive estimators with superior performance. Additionally, we leverage nested simulation frameworks with robust jackknife-based estimators and introduce a novel method combining nested simulation with Latin hypercube sampling for enhanced efficiency. For scenarios where experimental design is infeasible, we propose a partition-based approach enabling Sobol' index estimation from existing datasets, eliminating new experiment requirements. This extends into a comprehensive metamodeling framework supporting state-of-the-art estimators using available data. Finally, we introduce generalized Sobol' indices for quantifying global sensitivity in stochastic models with multivariate outputs.","abstract_html":"Sobol' indices are widely used in global sensitivity analysis to quantify input variable contributions to output variance in complex computational models. Traditional methods become impractical due to prohibitive computational costs, difficulties managing model stochasticity and multivariate outputs, and experimental design constraints. This dissertation addresses these limitations through advanced techniques based on metamodeling, multilevel Monte Carlo (MLMC) metamodeling, and nested simulation. We develop two joint metamodel-based estimators for Sobol' indices with established asymptotic normality, enabling reliable uncertainty quantification. Our proposed MLMC metamodeling approach for variance function estimation substantially reduces computational complexity, yielding competitive estimators with superior performance. Additionally, we leverage nested simulation frameworks with robust jackknife-based estimators and introduce a novel method combining nested simulation with Latin hypercube sampling for enhanced efficiency. For scenarios where experimental design is infeasible, we propose a partition-based approach enabling Sobol' index estimation from existing datasets, eliminating new experiment requirements. This extends into a comprehensive metamodeling framework supporting state-of-the-art estimators using available data. 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Traditional methods become impractical due to prohibitive computational costs, difficulties managing model stochasticity and multivariate outputs, and experimental design constraints. This dissertation addresses these limitations through advanced techniques based on metamodeling, multilevel Monte Carlo (MLMC) metamodeling, and nested simulation. We develop two joint metamodel-based estimators for Sobol' indices with established asymptotic normality, enabling reliable uncertainty quantification. Our proposed MLMC metamodeling approach for variance function estimation substantially reduces computational complexity, yielding competitive estimators with superior performance. Additionally, we leverage nested simulation frameworks with robust jackknife-based estimators and introduce a novel method combining nested simulation with Latin hypercube sampling for enhanced efficiency. For scenarios where experimental design is infeasible, we propose a partition-based approach enabling Sobol' index estimation from existing datasets, eliminating new experiment requirements. This extends into a comprehensive metamodeling framework supporting state-of-the-art estimators using available data. Finally, we introduce generalized Sobol' indices for quantifying global sensitivity in stochastic models with multivariate outputs."]},{"key":"dc:description.abstractgeneral","label":"General Abstract","values":["Computer models play a crucial role in analyzing complex systems across disciplines such as engineering, climate science, and healthcare. A central application is identifying which input factors most significantly influence model outcomes. Sobol' indices have become a standard approach for this task, offering a rigorous framework to quantify the global impact of input variations on outputs. However, traditional methods for estimating Sobol' indices often prove impractical for modern computational models due to their high computational cost, difficulties in handling stochastic and multi-output scenarios, and challenges associated with designed experiments. To overcome these challenges, we introduce a suite of advanced estimation techniques that enhance both efficiency and flexibility. Our approach boosts computational efficiency through the use of metamodeling, multilevel Monte Carlo, and nested simulation strategies. Additionally, we present a novel method for estimating Sobol' indices directly from existing datasets, eliminating the need for specially designed experiments. This is incorporated into a unified modeling framework that accommodates state-of-the-art estimators. Finally, we propose a generalized Sobol' index tailored for stochastic models with multivariate outputs, providing deeper insights into the sensitivity and behavior of complex systems."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Doctor of Philosophy"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["ETD"]},{"key":"dc:title","label":"Title","values":["Advances in Sobol' Index Estimation: Metamodeling, Multilevel Monte Carlo Metamodeling, and Nested Simulation Techniques"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Chen, Xi"],"dc:contributor.committeemember":["Tunc, Sait","Xu, Jie","L'Afflitto, Andrea"],"dc:contributor.department":["Industrial and Systems Engineering"],"dc:creator":["Zhang, Jingtao"],"dc:date.accessioned":["2025-08-29T08:00:18Z"],"dc:date.available":["2025-08-29T08:00:18Z"],"dc:date.issued":["2025-08-28"],"dc:description.abstract":["Sobol' indices are widely used in global sensitivity analysis to quantify input variable contributions to output variance in complex computational models. Traditional methods become impractical due to prohibitive computational costs, difficulties managing model stochasticity and multivariate outputs, and experimental design constraints. This dissertation addresses these limitations through advanced techniques based on metamodeling, multilevel Monte Carlo (MLMC) metamodeling, and nested simulation. We develop two joint metamodel-based estimators for Sobol' indices with established asymptotic normality, enabling reliable uncertainty quantification. Our proposed MLMC metamodeling approach for variance function estimation substantially reduces computational complexity, yielding competitive estimators with superior performance. Additionally, we leverage nested simulation frameworks with robust jackknife-based estimators and introduce a novel method combining nested simulation with Latin hypercube sampling for enhanced efficiency. For scenarios where experimental design is infeasible, we propose a partition-based approach enabling Sobol' index estimation from existing datasets, eliminating new experiment requirements. This extends into a comprehensive metamodeling framework supporting state-of-the-art estimators using available data. Finally, we introduce generalized Sobol' indices for quantifying global sensitivity in stochastic models with multivariate outputs."],"dc:description.abstractgeneral":["Computer models play a crucial role in analyzing complex systems across disciplines such as engineering, climate science, and healthcare. A central application is identifying which input factors most significantly influence model outcomes. Sobol' indices have become a standard approach for this task, offering a rigorous framework to quantify the global impact of input variations on outputs. However, traditional methods for estimating Sobol' indices often prove impractical for modern computational models due to their high computational cost, difficulties in handling stochastic and multi-output scenarios, and challenges associated with designed experiments. To overcome these challenges, we introduce a suite of advanced estimation techniques that enhance both efficiency and flexibility. Our approach boosts computational efficiency through the use of metamodeling, multilevel Monte Carlo, and nested simulation strategies. Additionally, we present a novel method for estimating Sobol' indices directly from existing datasets, eliminating the need for specially designed experiments. This is incorporated into a unified modeling framework that accommodates state-of-the-art estimators. Finally, we propose a generalized Sobol' index tailored for stochastic models with multivariate outputs, providing deeper insights into the sensitivity and behavior of complex systems."],"dc:description.degree":["Doctor of Philosophy"],"dc:format.medium":["ETD"],"dc:identifier.other":["vt_gsexam:44450"],"dc:identifier.uri":["https://hdl.handle.net/10919/137606"],"dc:language.iso":["en"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Global Sensitivity Analysis","Multilevel Monte Carlo","Nested Simulation","Metamodeling"],"dc:title":["Advances in Sobol' Index Estimation: Metamodeling, Multilevel Monte Carlo Metamodeling, and Nested Simulation Techniques"],"dc:type":["Dissertation"],"thesis:degree_discipline":["Industrial and Systems Engineering"],"thesis:degree_level":["doctoral"],"thesis:degree_name":["Doctor of Philosophy"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:19:39Z"}