Prof. Peter Chien, gave a lecture titled“Invariance-Preserving Emulation for Computer Models, with Application to Structural Energy Prediction”at AMSS on 30, September 2017.   

Computer models with invariance properties appear frequently in materials science, physics, biology and other fields. These properties are consequences of dependency on structural geometry, and cannot be accommodated by standard emulation methods. In this talk, he talked about that they would propose a new statistical framework for building emulators to preserve invariance. This framework used a weighted complete graph to represent the geometry and introduced a new class of function, called the relabeling symmetric functions, associated with the graph. They established a characterization theorem of the relabeling symmetric functions, and proposed a nonparametric kernel method for estimating such functions. The effectiveness of the proposed method was illustrated by several examples from materials science. 

Peter Chien is professor in Statistics at the University of Wisconsin-Madison. His research areas include uncertainty quantification, Big Data and design of experiments, with applications to engineering and the Internet. He received a National Science Foundation Career Award and an IBM Award. He has served on the editorial boards of Annals of Statistics, SIAM/ASA Journal of Uncertainty Quantification and other statistics journals.