Sequential Design and Analysis of High-Accuracy and Low-Accuracy Computer Codes
Shifeng Xiong, Peter Z. G. Qian, Cheng Feng Wu · Technometrics · 2012
Shifeng Xionga, Peter Z. G. Qianb & C. F. Jeff Wuc a Academy of Mathematics and Systems Science , Chinese Academy of Sciences , Beijing , 100190 , China b Department of Statistics , University of Wisconsin-Madison , Madison , WI , 53706 , USA c H. Milton Stewart School of Industrial and Systems Engineering , Georgia Institute of Technology , Atlanta , GA , 30332-0205 , USA A growing trend in engineering and science is to use multiple computer codes with different levels of accuracy to study the same complex system. We propose a framework for sequential design and analysis of a pair of high-accuracy and low-accuracy computer codes. It first runs the two codes with a pair of nested Latin hypercube designs (NLHDs). Data from the initial experiment are used to fit a prediction model. If the accuracy of the fitted model is less than a prespecified threshold, the two codes are evaluated again with input values chosen in an elaborate fashion so that their expanded scenario sets still form a pair of NLHDs. The nested relationship between the two scenario sets makes it easier to model and calibrate the difference between the two sources. If necessary, this augmentation process can be repeated a number of times until the prediction model based on all available data has reasonable accuracy. The effectiveness of the proposed method is illustrated with several examples. Matlab codes are provided in the online supplement to this article.