Stochastic sampling using moving least squares response surface approximations

Abstract

This work discusses the simulation of samples from a target probability distribution which is related to the response of a system model that is computationally expensive to evaluate. Implementation of surrogate modeling, in particular moving least squares (MLS) response surface methodologies, is suggested for efficient approximation of the model response for reduction of the computational burden associated with the stochastic sampling. For efficient selection of the MLS weights and improvement of the response surface approximation accuracy, a novel methodology is introduced, based on information about the sensitivity of the sampling process with respect to each of the model parameters. An approach based on the relative information entropy is suggested for this purpose, and direct evaluation from the samples available from the stochastic sampling is discussed. A novel measure is also introduced for evaluating the accuracy of the response surface approximation in terms relevant to the stochastic sampling task.