Revised: 26 Dec 2014

Statistics 330/600 (Spring 2015)

Advanced Probability

Instructor: David Pollard
When: Tuesday, Thursday 2:30 - 3:45
Where: 24 Hillhouse, main classroom
Office hours: Initially, immediately after each lecture. More times to be added if needed.
TA: Dana Yang
Problem session: To be arranged if needed
Other: courses taught by DP in previous years
Short description: Measure theoretic probability, conditioning, laws of large numbers, convergence in distribution, characteristic functions, central limit theorems, martingales. Some knowledge of real analysis is assumed.
Intended audience: The course is aimed at students (both graduate and undergraduate) who are either comfortable with real analysis or who are prepared to invest some extra effort to learn more real analysis during the course. Prior exposure to an introductory probability course (such as Stat 241/541) would be an advantage, but is not essential.

Knowledge of measure theory is not assumed. The first two weeks of the course will introduce key measure theoretic ideas, with other ideas explained as needed.

Text: Pollard, User's Guide to Measure Theoretic Probability Cambridge University Press 2001.

A sample: UGMTP-extract = first two chapters from UGMTP, plus a rewrite of section 2.11 (replacing cones by vector spaces). Ignore old 2.11.

If you prefer a more standard text, one of the books on the list of references might be to your taste.

Topics: Coverage similar to the description at the end of the Preface, which follows the Table of Contents of UGMTP.
Grading: The final grade will be based entirely on the weekly homework, which is due each Thursday.

Students who wish to work in teams (no more than 2 to a team) should submit a single solution set. Each member of a team will be expected to understand the team's solutions sufficiently well to explain the reasoning at the blackboard. Occasional meetings with DP will be arranged. Teams are expected to work independently of each other.

Other resources:
  • Handouts, including some extracts from UGMTP and rewrites of UGMTP and some advice for those who want to use LaTeX.
  • Class materials for an introductory probability course (Stat 241/541, Fall 2014), containing more extensive elementary discussion of probabilistic ideas.