報告題目：Penalized Projected Kernel Calibration for Computer Models

報告所屬學科：管理科學與工程

報告人：王彥（北京工業大學）

報告時間：2021年3月30日 10:00

報告地點：經管學院707室

報告摘要：

Projected kernel calibration is known to be theoretically superior, its loss function is abbreviated as PK loss function. In this work, we prove the uniform convergence of PK loss function and show that (1) when the sample size is large, any local minimum point and local maximum point of the $L_2$ loss between the true process and the computer models is a local minimum point of the PK loss function; (2) all the local minimum values of the PK loss function converge to the same value. These theoretical results imply that it is extremely hard for the projected kernel calibration to identify the global minimum point of the $L_2$ loss which is defined as the optimal value of the calibration parameters. To solve this problem, a frequentist method, called the penalized projected kernel calibration method is proposed. As a frequentist method, the proposed method is proved to be semi-parametric efficient. On the other hand, the proposed method has a natural bayesian version, which allows users to calculate the credible region of the calibration parameters without using a large sample approximation. Through extensive simulation studies and a real-world case study, we show that the proposed calibration can accurately estimate the calibration parameters, and compare favorably to alternative calibration methods regardless of the sample size.

報告人簡介：

王彥博士現為北京工業大學統計與數據科學學院助理教授。2018年在中國科學院數學與系統科學研究院獲得博士學位。2017年應吳建福教授邀請訪問佐治亞理工學院工業工程系。2018年應Prof Tan Matthias Hwai-yong邀請訪問香港城市大學系統與管理工程系。研究方向包括：計算機模型校準與糾偏；計算機模型全局最優化；非參數統計；不確定性量化等方向。