The Statistics Seminar Speaker for Wednesday, May 4, 2016, is Ian McKeague, a professor in the Department of Biostatistics at Columbia. Ian has a B.A., M.A. and M.Math from the University of Cambridge, and a Ph.D. in statistics from the University of North Carolina at Chapel Hill in 1980. He was on the faculty of the Department of Statistics of the Florida State University, 1980-2004.
He was on sabbatical leave at the Mathematical Sciences Research Institute of the University of California at Berkeley, and then at the Laboratoire de Modélisation et Calcul of the Université Joseph Fourier, Grenoble, France, 1991-1992. He served as Chair of the FSU Statistics department, 1996-99, and was named the Ralph A. Bradley Professor of Statistics at FSU in 2000. He has been a Professor of Biostatistics at Columbia University since 2004.
His research interests include empirical likelihood, statistical methods in physical oceanography, functional data analysis, inference for stochastic processes, survival analysis, competing risks models for HIV/AIDS data, Markov chain Monte Carlo and Bayesian methods, simultaneous inference, efficient estimation for semiparametric models, missing data, counting processes and spatial point processes. He has served as an associate editor of the Annals of Statistics for seven years, the Journal of the American Statistical Association for eight years, and is currently serving on the editorial boards of the Journal of the American Statistical Association, Statistical Inference for Stochastic Processes, and the International Journal of Biostatistics. He is a fellow of the Institute of Mathematical Statistics and a fellow of the American Statistical Association.
Title: Stein’s Method, Many Interacting Worlds and Quantum Mechanics
Abstract: Hall, Deckert and Wiseman (2014) recently proposed that quantum theory can be understood as the continuum limit of a deterministic theory in which there is a large, but finite, number of classical “worlds.” A resulting Gaussian limit theorem for particle positions in the ground state, agreeing with quantum theory, was conjectured by these authors and proven by McKeague and Levin (2015, arXiv:1412.1563) using Stein’s method. In this talk we discuss new connections between Stein’s method and Many Interacting Worlds theory. In particular, we show that quantum position probability densities for higher energy levels beyond the ground state arise as distributional fixed points in a new generalization of Stein’s method. These are then used to obtain a rate of distributional convergence for conjectured particle positions in the first energy level above the ground state to the (two-sided) Maxwell distribution. The talk is based on joint work with Erol Pekoz and Yvik Swan.
Refreshments will be served after the seminar in 1181 Comstock Hall.