Bayesian estimation of probabilistic sensitivity measures

Abstract

Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest. Simulation complexity, large dimensionality and long running times may force analysts to make statistical inference at small sample sizes. Methods designed to estimate probabilistic sensitivity measures at relatively low computational costs are attracting increasing interest. We propose a fully Bayesian approach to the estimation of probabilistic sensitivity measures based on a one-sample design. We discuss, first, new estimators based on placing piecewise constant priors on the conditional distributions of the output given each input, by partitioning the input space. We then present two alternatives, based on Bayesian non-parametric density estimation, which bypass the need for predefined partitions. In all cases, the Bayesian paradigm guarantees the quantification of uncertainty in the estimation process through the posterior distribution over the sensitivity measures, without requiring additional simulator evaluations. The performance of the proposed methods is compared to that of traditional point estimators in a series of numerical experiments comprising synthetic but challenging simulators, as well as a realistic application. $\textit{An Updated Version of the Manuscript is Forthcoming in Statistics and Computing.}$