This thesis proposes a least squares formulation to determine a set of empirical importance weights to achieve a change of probability measure. The objective of the thesis is to estimate statistics from a target distribution - distribution of interest using random samples generated from a different proposal distribution - cheap/available distribution. The approach taken here works directly with the probability measure of the proposal and target distributions, for which only samples from each are needed. The result is an approach more capable of achieving high dimensional probability measure change than current state-of-the-art methods. Such a method can enable efficient and accurate propagation of uncertainty through model chains of unknown input and output regularity, such as those often encountered in process-structure-property chains in materials science. The proposed approach is demonstrated on five benchmark problems of increasing dimension and also tested on a Gas Turbine System.
