Cases for the nugget in modeling computer experiments

TL;DR

This paper argues that including a non-zero nugget in Gaussian process models for computer experiments improves their statistical properties, challenging the traditional view that computer experiments are deterministic and should omit the nugget.

Contribution

It demonstrates that estimating a non-zero nugget enhances surrogate model accuracy and coverage, offering a new perspective on modeling deterministic computer experiments.

Findings

Estimating a non-zero nugget improves predictive accuracy.

Including a nugget enhances model coverage.

Traditional models often omit the nugget, which can be suboptimal.

Abstract

Most surrogate models for computer experiments are interpolators, and the most common interpolator is a Gaussian process (GP) that deliberately omits a small-scale (measurement) error term called the nugget. The explanation is that computer experiments are, by definition, "deterministic", and so there is no measurement error. We think this is too narrow a focus for a computer experiment and a statistically inefficient way to model them. We show that estimating a (non-zero) nugget can lead to surrogate models with better statistical properties, such as predictive accuracy and coverage, in a variety of common situations.