Robust simulation design for generalized linear models in conditions of heteroscedasticity or correlation

TL;DR

This paper develops a robust design methodology for computer experiments with heteroscedastic or correlated outputs, explicitly modeling variance and correlation structures to improve efficiency in simulation-based meta-modeling.

Contribution

It introduces a computational approach that incorporates variance and correlation structures into the meta-model, enabling robust experimental design without assuming error independence.

Findings

Method effectively accounts for heteroscedasticity and correlation.

Design optimization improves meta-model accuracy and efficiency.

Applicable to complex simulation scenarios with dependent errors.

Abstract

A meta-model of the input-output data of a computationally expensive simulation is often employed for prediction, optimization, or sensitivity analysis purposes. Fitting is enabled by a designed experiment, and for computationally expensive simulations, the design efficiency is of importance. Heteroscedasticity in simulation output is common, and it is potentially beneficial to induce dependence through the reuse of pseudo-random number streams to reduce the variance of the meta-model parameter estimators. In this paper, we develop a computational approach to robust design for computer experiments without the need to assume independence or identical distribution of errors. Through explicit inclusion of the variance or correlation structures into the meta-model distribution, either maximum likelihood estimation or generalized estimating equations can be employed to obtain an appropriate Fisher information matrix. Robust designs can then be computationally sought which maximize some relevant summary measure of this matrix, averaged across a prior distribution of any unknown parameters.