BAYESIAN OPTIMAL DESIGN OF EXPERIMENTS FOR EXPENSIVE BLACK-BOX FUNCTIONS UNDER UNCERTAINTY

Abstract

Researchers and scientists across various areas face the perennial challenge of selecting experimental conditions or inputs for computer simulations in order to achieve promising results. The aim of conducting these experiments could be to study the production of a material that has great applicability. One might also be interested in accurately modeling and analyzing a simulation of a physical process through a high-fidelity computer code. The presence of noise in the experimental observations or simulator outputs, called aleatory uncertainty, is usually accompanied by limited amount of data due to budget constraints. This gives rise to what is known as epistemic uncertainty. This problem of designing of experiments with limited number of allowable experiments or simulations under aleatory and epistemic uncertainty needs to be treated in a Bayesian way. The aim of this thesis is to extend the state-of-the-art in Bayesian optimal design of experiments where one can optimize and infer statistics of the expensive experimental observation(s) or simulation output(s) under uncertainty.