Once upon a time I decided to update the empirical process material in my 1984 and 1990 books. I needed some brief document that I could, in good conscience, recommend to students who wanted to understand some of the main ideas about empirical processes, including improvements made in the last twenty years. The manuscript had the working title Asymptopia. Unfortunately, the longer I labored the further I seemed from my objective.

A few years ago I decided I might actually finish if I split the Asymptopia manuscript into two parts. Currently I am working on the empirical process bit, which has acquired the temporary working title Mini Empirical. Some chapters have reached a reasonably complete form. Those chapters are in the Mini subdirectory.

March 2022

I am still struggling with the book. The emphasis has changed from limit theorems to inequalities. As I am no longer teaching, I no longer have the benefit of discovering errors as I try to explain ideas in class. In particular, I am very worried about the BinFriends chapter. The arguments there are elementary but subtle. While I was working on that chapter, every time I found a new mistake and fixed it another part of the argument would break.

October 2023

Still struggling. The working title is now Pttm = Probability tools, tricks, and miracles. At the moment the manuscript runs to a little over 400 pages. (See current table of contents.) Chapters 2 through 12 are in what I hope is final form. The other chapters still need a lot of editing.

	Name	Last modified	Size	Description
	Parent Directory		-
	1984book/	2008-07-04 20:53	-
	Iowa/	2017-01-19 21:14	-
	LeCamFest/	2017-01-19 21:12	-
	Mini/	2022-03-26 16:21	-
	Pttm/	2024-06-14 13:35	-
	UGMTP/	2017-01-19 21:15	-
	oldHEADER.html	2017-01-19 17:33	890

Pollard Lectures 2023

• Time: Fridays 1:00--2:15, starting 6 October 2023
• Place: Kline Tower Room 1327

For many years I have have been working on a manuscript, tentatively called Probability tools, tricks, and miracles, that collects together a range of ideas that have been useful to me while working on statistical problems. My aim has been to simplify and, where possible, improve and extend a collection of tools that are scattered throughout the literature. I have also tried to understand why particular methods work and what limitations they have.

At the moment the manuscript runs to a little over 400 pages. (See current table of contents.) Chapters 2 through 12 are in what I hope is final form. The other chapters still need a lot of editing. Unfortunately, I have not yet had a chance to test the ideas on a live audience. Hence this set of 5 lectures.

I'll be assuming a little bit of 600-level probability. (For example, I want to explain convexity of the log MGF by means of an exponential tilting.) I also want to use P instead of E, of course. My aim is to convey the main ideas, leaving it up to the enthusiastic to read the details in my manuscript. I also plan to hang around after the lectures in case anyone wants to dig more deeply into the material.

My current plan:

• (2 lectures?) Tail bounds from MGF's (moment generating functions). Standard cases (eg, N(0,1) and Poisson) and cases where we have good upper bounds for the MGF (eg. Hoeffding and Bennett). Extensions to martingales (eg. bounded differences). See attached chapter, MGF.pdf.
• (1 lecture?) Path methods for the multivariate normal. Concentration of lipschitz functions under the N(0, I_n). Concentration of the maximum for a general multivariate normal. Maybe, mention comparison methods (eg. Fernique). See attached chapter, Gaussian.pdf.
• (2 lectures?) Chaining constructions. Why does it work? Classical packing/covering number constructions. Maybe mention some of the fancier methods derived from the 'majorizing measure' idea.

More lectures would be needed if anyone wanted to hear about VC classes and their modern extensions, or if anyone wanted to get into the details related to majorizing measures and Talagrand's "generic chaining".