Uncertainty Quantification Using Epi-Splines and Soft Information

Abstract

This thesis deals with the problem of measuring system performance in the presence of uncertainty. The system under consideration may be as simple as an Army vehicle subjected to a kinetic attack or as complex as the human cognitive process. Information about the system performance is found in the observed data points, which we call hard information, and may be collected from physical sensors, field test data, and computer simulations. Soft information is available from human sources such as subject-matter experts and analysts, and represents qualitative information about the system performance and the uncertainty present. We propose the use of epi-splines in a nonparametric framework that allows for the systematic integration of hard and soft information for the estimation of system performance density functions in order to quantify uncertainty. We conduct empirical testing of several benchmark analytical examples, where the true probability density functions are known. We compare the performance of the epi-spline estimator to kernel-based estimates and highlight a real-world problem context to illustrate the potential of the framework.