Dr. Dan Keenan, Professor Emeritus, UVa Statistics

Friday, December 3, 2021

12:00 noon

New Cabell 309

Some Things Gleaned From a 40+ Year Research Career 

 

ABSTRACT

As part of the Introduction and a “thread” that runs throughout a book on Advanced Probability and Mathematical Statistics that I may or may not ever finish, I discuss several observations that I came to realize as being quite fundamental to the breadth and depth of the evolution of these disciplines.  One of the observations is the delicate balance in the division between finite, countably infinite and uncountable; the issue of the existence of regular conditional probability and disintegration, which many argue are the foundation of modern probability and mathematical statistics, is an example of the above delicate balance, as is the Bayesian preference for finite additivity.  Other observations include the importance of semigroup structure (e.g., convolution of measures) and contraction; the meaning and the modeling of “noise” (paradigm: data=model + noise); regularization; and the importance of trigonometric polynomials and L2 isometries.  In this talk, I’ll discuss some of these observations.