Randomized sobol’ sensitivity indices

Abstract

Classical Sobol’ sensitivity indices assume the distribution of a model’s parameters is known completely for a given model, but this is usually difficult to measure in practical problems. What is measurable is the distribution of parameters for a particular data set, and the Sobol’ indices can significantly vary as different data sets are used in the estimation of the parameter distributions. To address this issue, we introduce a hierarchical probabilistic framework where Sobol’ sensitivity indices are random variables. An ANOVA decomposition in this hierarchical framework is given. Some analytical examples and an application to interest rate modeling illustrate the use of the randomized Sobol’ indices framework.