Optimal design for parameter estimation in Gaussian process regression models with input-dependent noise is examined. The motivation stems from the area of computer experiments, where computationally demanding simulators are approximated using Gaussian process emulators to act as statistical surrogates. In the case of stochastic simulators, which produce a random output for a given set of model inputs, repeated evaluations are useful, supporting the use of replicate observations in the experimental design. The findings are also applicable to the wider context of experimental design for Gaussian process regression and kriging. Designs are proposed with the aim of minimising the variance of the Gaussian process parameter estimates. A heteroscedastic Gaussian process model is presented which allows for an experimental design technique based on an extension of Fisher information to heteroscedastic models. It is empirically shown that the error of the approximation of the parameter variance by the inverse of the Fisher information is reduced as the number of replicated points is increased. Through a series of simulation experiments on both synthetic data and a systems biology stochastic simulator, optimal designs with replicate observations are shown to outperform space-filling designs both with and without replicate observations. Guidance is provided on best practice for optimal experimental design for stochastic response models.
Bibliographical noteNOTICE: this is the author’s version of a work that was accepted for publication in Computational statistics and data analysis. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Boukouvalas, A, Cornford, D & Stehlík, M, 'Optimal design for correlated processes with input-dependent noise' Computational statistics and data analysis, vol. 71 (2014) DOI http://dx.doi.org/10.1016/j.csda.2013.09.024
Funding: EPSRC/RCUK - MUCM Basic Technology
Supplementary material: http://dx.doi.org/10.1016/j.csda.2013.09.024
- optimal design of experiments
- correlated observations