Model guided adaptive design and analysis in computer experiment

Abstract

Computer experiments have become increasingly important in several different industries. These experiments save resources by exploring different designs without necessitating real hardware manufacturing. However, computer experiments usually require lengthy simulation times and powerful computational capacity. Therefore, it is often pragmatically impossible to run experiments on a complete design space. In this paper, we propose an adaptive sampling scheme that interactively works with predictive models to sequentially select design points for computer experiments. The selected samples are used to build predictive models, which in turn guide further sampling and predict the entire design space. For illustration, we use Bayesian additive regression trees (BART), multiple additive regression trees (MART), treed Gaussian process and Gaussian process to guide the proposed sampling method. Both real data and simulation studies show that our sampling method is effective in that (i) it can be used with different predictive models; (ii) it can select multiple design points without repeatedly refitting the predictive models, which makes parallel simulations possible and (iii) the predictive model built on its generated samples gives more accurate predictions on the unsampled points than the models built on samples from other methods such as random sampling, space‐filling designs and some adaptive sampling methods. © 2012 Wiley Periodicals, Inc. Statistical Analysis and Data Mining, 2012