Cases for the nugget in modeling computer experiments

By Robert B. Gramacy, Herbert K. H. Lee. Statistics and computing, 2010

303 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/59eccbff80ecf6e16fd6211f57ae5b84e9931189

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In Computational Theory and Mathematics

In Management Science and Operations Research

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Citations in the corpus

Quantile-Based Optimization of Noisy Computer Experiments With Tunable Precision (2013, methodology): “A more rigorous alternative, as noted by Gramacy and Lee (2010b) and Gramacy and Polson (2011), consists of computing the EI based on the joint distribution of (min(Y (X)), Y (x)) conditional on Ãn; however, in this form, the EI must be estimated by expensive Monte Carlo simulations, which makes the”
Composite Gaussian process models for emulating expensive functions (2012, methodology): “To emulate deterministic outputs from computer experiments, Gramacy and Lee (2012) advocate always including a nonzero nugget in the kriging predictor for reasons even beyond computations.”
Local Gaussian Process Approximation for Large Computer Experiments (2013, methodology): “ achieved with the greedy method if so desired. Although some recent papers have argued that the quest for truer interpolation in surrogate modeling may not be ecient from a statistical perspective (Gramacy and Lee, 2011a; Peng and Wu, 2012), seeking out the smallest possible nugget while retaining ”
Practical options for selecting data-driven or physics-based prognostics algorithms with reviews (2015, background): “Also, the nugget effect representing the noise in data is sometimes considered by adding a value greater than zero to the diagonal terms of the covariance matrix, so that the simulated outputs do not pass noisy data points [95,96].”
Remarks on multi-output Gaussian process regression (2018, background): “[33] argued that this is a too narrow and statistically inefficient way to approximate the underlying function.”
Bayesian Solution Uncertainty Quantification for Differential Equations (2013, background): “Currently, numerical uncertainty is largely ignored when emulating a computer model, although it is informally incorporated through a covariance nugget (see, e.g., Gramacy and Lee, 2012) whose magnitude is often chosen heuristically.”
Multi-output separable Gaussian process: Towards an efficient, fully Bayesian paradigm for uncertainty quantification (2013, background): “Apart from improving the stability of the computations, one can argue that the presence of the nugget can also lead to better predictive accuracy [31].”
Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantification (2018, methodology): “For the generated training data, a priori we assume that the noise variance (also known as nugget [54]) to be very small e.”
A General Framework for Vecchia Approximations of Gaussian Processes (2017, methodology): “The noisy-observation assumption is ubiquitous in spatial statistics, GP regression, and functional data, and has been proposed for the modeling of computer experiments (Gramacy and Lee, 2012).”
Design of computer experiments: space filling and beyond (2011, unknown): “Gramacy and Lee (2010) for other motivations concerning the introduction of a nugget effect.”