Optimal design for correlated processes with input-dependent noise

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

D-optimal designs via a cocktail algorithm

A fast new algorithm is proposed for numerical computation of (approximate) D-optimal designs. This "cocktail algorithm" extends the well-known vertex direction method (VDM; Fedorov 1972) and the multiplicative algorithm (Silvey, Titterington and Torsney, 1978), and shares their simplicity and monotonic convergence properties. Numerical examples show that the cocktail algorithm can lead to dramatically improved speed, sometimes by orders of magnitude, relative to either the multiplicative algorithm or the vertex exchange method (a variant of VDM). Key to the improved speed is a new nearest neighbor exchange strategy, which acts locally and complements the global effect of the multiplicative algorithm. Possible extensions to related problems such as nonparametric maximum likelihood estimation are mentioned.Comment: A number of changes after accounting for the referees' comments including new examples in Section 4 and more detailed explanations throughou

Bias in nonlinear regression models with constrained parameters

Rapport technique 1997-4*INRA, Centre de Versailles-Grignon (FRA) Diffusion du document : INRA, Centre de Versailles-Grignon (FRA)International audienc

Measures of nonlinearity for biadditive models

Rapport technique, 22 ref. *INRA Biométrie 78352 Jouy-en-Josas (FRA) Diffusion du document : INRA Biométrie 78352 Jouy-en-Josas (FRA)National audienc

Biadditive ANOVA models: Reminders and asymptotical bias

Rapport technique 1998-4*INRA, Centre de Versailles-Grignon (FRA) Diffusion du document : INRA, Centre de Versailles-Grignon (FRA)International audienc

Properties of nonlinear regression models with nonlinear parameter constraints

International audienc

Bias in nonlinear regression models with constrained parameters

Rapport technique 1997-4*INRA, Centre de Versailles-Grignon (FRA) Diffusion du document : INRA, Centre de Versailles-Grignon (FRA)International audienc

Measures of nonlinearity for a biadditive ANOVA model

International audienc