A computer model can be used for predicting an output only after specifying the values of some unknown physical constants known as calibration parameters. The unknown calibration parameters can be estimated from real data by conducting physical experiments. This paper presents an approach to optimally design such a physical experiment. The problem of optimally designing physical experiment, using a computer model, is similar to the problem of finding optimal design for fitting nonlinear models. However, the problem is more challenging than the existing work on nonlinear optimal design because of the possibility of model discrepancy, that is, the computer model may not be an accurate representation of the true underlying model. Therefore, we propose an optimal design approach that is robust to potential model discrepancies. We show that our designs are better than the commonly used physical experimental designs that do not make use of the information contained in the computer model and other nonlinear optimal designs that ignore potential model discrepancies. We illustrate our approach using a toy example and a real example from industry.
Calibration Strategies for Robust Causal Estimation: Theoretical and Empirical Insights on Propensity Score-Based Estimators
Economic AI, Nürnberger Str. 262 A, 93059 Regensburg, Bayern, Germany（经济人工智能，德国雷根施塔特）；Chair of Statistics with Application in Business Analytics, University of Hamburg Business School, Moorweidenstr. 18, 20148 Hamburg, Hamburg, Germany（商务分析统计学系，汉堡大学商业学院）；Chair of Mathematics and Statistics in Economics, University of Hamburg Business School, Von-Melle-Park 5, 20146 Hamburg, Hamburg, Germany（经济学数学与统计学系，汉堡大学商业学院）；Düsseldorf Institute for Competition Economics, Heinrich Heine University Düsseldorf, Universitätstr. 1, 20225 Düsseldorf, Nordrhein-Westphalen, Germany（多特蒙德竞争经济学研究所，杜伊斯堡-艾森大学）
Discrepancy Modeling with Intermediate Variables: A New Framework for Robust Gaussian Process Calibration
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；Argonne National Laboratory（阿贡国家实验室）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
