Alexis Boukouvalas, Dan Cornford, Milan Stehlik,
"Optimal design for correlated processes with input-dependent noise"
, in Computational Statistics and Data Analysis, Vol. 71, Seite(n) 1088?1102, 2014, ISSN: 1872-7352
Original Titel:
Optimal design for correlated processes with input-dependent noise
Sprache des Titels:
Englisch
Original Kurzfassung:
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.
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