Prof. Murray Aitkin   

School of Mathematics and Statistics, University of Melbourne, Australia

Speech Title: Getting the precisions right in complex models: precisions from models and the bootstrap 

Abstract

In any applied statistics project, the statistician worries about uncertainty and quantifies it by modelling data as  realisations generated from a probability space.

Another approach to uncertainty quantification is to find similar data sets and then use the variability of results between these data sets to capture the uncertainty.

The first approach is through probability model-based likelihood analysis, due to R.A. Fisher.

The second approach is through ``model-free" extensions of least squares and repeated sampling, due to  J. Neyman and B. Efron.

Inferential tools in machine learning are based on extensions of low-degree least squares: higher-level variability is represented by splines -- small non-linear terms at break-points where slopes or curvatures change suddenly.

The precision of the spline or other least squares procedure is assessed through the bootstrap  resampling of the data. The bootstrap has been recently shown (Aitkin 2023  pp. 178-180)  to be  ineffective in assessing precision.

We need a different model-free procedure for precisions: the Bayesian bootstrap.

We compare model-based and ``model-free” procedures for precision in some complex models.

Reference: Aitkin M. (2023) Introduction to Statistical Modelling and Inference. CRC Press, Boca Raton

Biography

Prof. Murray Aitkin trained in mathematical statistics (BSC, PhD, DSc) at the University of Sydney and did postdoctoral work at the Thurstone Psychometrics Laboratory in Chapel Hill. In 1969, he joined the School of behavioral Sciences at Macquarie University, where he established a small statistical advisory group. 1971-1972 spent a year visiting the Educational Testing Service as a Fulbright Senior Fellow, and in 1976 accepted the SSRC Professorship in Social Science Statistics at Lancaster University in the United Kingdom. Later, he was appointed Lancaster Professor of Applied Statistics and Director of the Foundation for the Centre for Applied Statistics. The Centre has extensive research and advisory links with the strong social sciences department at Lancaster University.

In 1986, he was appointed a visiting scholar at the Educational Testing Service. He returned to Tel Aviv as a professor of statistics at the School of Mathematical Sciences. In 1992, he was awarded an ARC Advanced Research Fellowship and was subsequently appointed Professor of statistics at the University of Newcastle in the UK, retiring early in 2004. From 2000 to 2002, I was chief statistician at the Institute for Educational Statistical Services, a division of the American Institute that advises the U.S. Department of Education's National Center for Education Statistics, in Washington, D.C. After 2002, he continued to work as a consultant for NCES in Newcastle and in Melbourne. He was an Emeritus Professor in the Department of Psychology (2004-2008) and the School of Mathematics and Statistics (2008-present) at the University of Melbourne.