Bootstrapping and Jackknife Resampling to Improve Sparse-Sample UQ Methods for Tail Probability Estimation

Tolerance Interval Equivalent Normal (TI-EN) and Superdistribution (SD) sparse-sample uncertainty quantification (UQ) methods are used for conservative estimation of small tail probabilities. These methods are used to estimate the probability of a response laying beyond a specified threshold with limited data. The study focused on sparse-sample regimes ranging from N = 2 to 20 samples, because this is reflective of most experimental and some expensive computational situations. A tail probability magnitude of 10−4 was examined on four different distribution shapes, in order to be relevant for quantification of margins and uncertainty (QMU) problems that arise in risk and reliability analyses. In most cases the UQ methods were found to have optimal performance with a small number of samples, beyond which the performance deteriorated as samples were added. Using this observation, a generalized Jackknife resampling technique was developed to average many smaller subsamples. This improved the performance of the SD and TI-EN methods, specifically when a larger than optimal number of samples were available. A Complete Jackknifing technique, which considered all ∗Sandia National Laboratories document SAND2019-3256 C. This paper is a work of the United States Government and is not subject to copyright protection in the U.S. †Address all correspondence to this author. ‡Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energys National Nuclear Security Administration under contract DENA0003525. possible sub-sample combinations, was shown to perform better in most cases than an alternative Bootstrap resampling technique.