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Tuesday, February 05
Experimental Design, Model Calibration, and
Roshan J. Vengazhiyil and C. F. Jeff Wu, Georgia Institute of Technology, Atlanta
Computer Science and Mathematics Division Seminar
10:00 AM — 11:00 AM, Building 4500-N, Hiwassee Conference Room (K-235)
Contact: Billy Fields (email@example.com), 865.241.0212
AbstractWe will start the talk with a newly developed space-filling design, called minimum energy design (MED). The key ideas involved in constructing the MED are the visualization of each design point as a charged particle inside a box, and minimization of the total potential energy of these particles. It is shown through theoretical arguments and simulations, that under regularity conditions and proper choice of the charge function, the MED can asymptotically generate any arbitrary probability density function. This new design technique has important applications in Bayesian computation and uncertainty quantification. The second part of the talk will focus on model calibration. The commonly used Kennedy and O'Hagan's (KO) approach treats the computer model as a black box and therefore, the statistically calibrated models lack physical interpretability. We propose a new framework that opens up the black box and introduces statistical models inside the computer model. This approach leads to simpler models that are physically more interpretable. Then, we will present some theoretical results concerning the convergence properties of calibration parameter estimation in the KO formulation of the model calibration problem. The KO calibration is shown to be asymptotically inconsistent. A new approach, called L2 distance calibration, is shown to be consistent and asymptotically efficient in estimating the calibration parameters.