Cases for the nugget in modeling computer experiments

Authors:
Robert B. Gramacy;Herbert K. Lee
Affiliations:
Booth School of Business, University of Chicago, Chicago, USA;Applied Math & Statistics, University of California, Santa Cruz, Santa Cruz, USA
Venue:
Statistics and Computing
Year:
2012

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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.