Automatic Estimation of Sobol' Indices Based on Quasi-Monte Carlo Methods

• Activity Number: 427
• Type: Contributed
• Date/Time: Tuesday, August 2, 2016 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Lluís Antoni Jiménez Rugama* and Laurent Gilquin and Clémentine Prieur and Elise Arnaud and Hervé Monod and Fred Hickernell
• Companies: Illinois Institute of Technology and Université de Grenoble Alpes and Université de Grenoble Alpes and Université de Grenoble Alpes and Institut National de la Recherche Agronomique and Illinois Institute of Technology
• Keywords: quasi-Monte Carlo ; Sobol indices ; sensitivity analysis ; numerical integration ; automatic algorithms

Abstract

In this talk we will introduce a new estimation for the Sobol' indices based on quasi-Monte Carlo methods. Sobol' indices are a variance based sensitivity analysis developed by Ilya M. Sobol'. Given a random variable Y as a function of another set of random variables, these indices measure what part of the variance of Y is explained by each set of input variables. In addition, we will discuss the origin of the quasi-Monte Carlo integration error, and propose a new automatic algorithm that estimates the indices. The key point of the algorithm is that it will find the number of integration points itself, and return the estimate with an error no greater than the user specified tolerance.