Nonparametric estimation of probabilistic sensitivity measures

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 first, propose new estimators based on a one-sample design and building on the idea of placing piecewise constant Bayesian priors on the conditional distributions of the output given each input, after partitioning the input space. We then present two alternatives, based on Bayesian non-parametric density estimation, which bypass the need for predefined partitions. Quantification of uncertainty in the estimation process through is possible without requiring additional simulator evaluations via Bootstrap in the simplest proposal, or from the posterior distribution over the sensitivity measures, when the entire inferential procedure is Bayesian. 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.