Discussion: "Bayesian Optimal Design of Experiments for Inferring the Statistical Expectation of Expensive Black-Box Functions" (Pandita, P., Bilionis, I., and Panchal, J., 2019. ASME. J. Mech. Des. 141(10): 101404)

TL;DR

This paper discusses improvements to Bayesian optimal experiment design for estimating the expectation of expensive black-box functions, simplifying the acquisition function and extending its applicability to arbitrary input distributions.

Contribution

It simplifies the acquisition function by showing the last three terms sum to zero and generalizes the analytical computation to any input distribution.

Findings

The last three terms of the acquisition sum to zero.

Analytical computation can be extended to arbitrary input distributions.

The framework's applicability is significantly broadened.

Abstract

The authors of the discussed paper simplified the information-based acquisition on estimating statistical expectation and developed analytical computation for each involved quantity under uniform input distribution. In this discussion, we show that (1) the last three terms of the acquisition always add up to zero, leaving a concise form with a much more intuitive interpretation of the acquisition; (2) the analytical computation of the acquisition can be generalized to arbitrary input distribution, greatly broadening the application of the developed framework.