RESEARCH TOPICS IN STOCHASTIC PROCESSES:
PERFECT MCMC ALGORITHMS
(STA 4247S, Spring 2001)
Time and place:
Wednesdays, 1:00 to 3:00 p.m.
First class January 10; last class April 11; no class February 21
(Reading Week). Wetmore Hall (300 Huron St.), room 75.
Instructor:
Professor Jeffrey S. Rosenthal,
Department of Statistics, University of Toronto
Office hours Thursdays 2:00-3:30, or after class, or by appointment,
or any other time you can find me.
Sidney Smith Hall, room 6024; phone (416) 978-4594; contact me;
http://markov.utstat.toronto.edu/jeff/
Topic:
We will explore "perfect" or "exact" Markov chain Monte Carlo (MCMC)
algorithms. This is a recent and exciting research development in the
theory of stochastic processes.
Reference:
D.B. Wilson's annotated
bibliography of exact MCMC research papers, available on-line at
http://dimacs.rutgers.edu/~dbwilson/exact/
and the research papers described there.
Course Outline:
During the first few weeks, the instructor will explain the basics of
Markov chain Monte Carlo (MCMC) algorithms, coupling from the past
(CFTP), Fill's algorithm, etc. In the remaining weeks, students will
read and present (and write about) recent research papers which further
develop these algorithms, in both theory and application.
Requirements:
Students will be expected to select certain research material (in
consultation with the instructor); read and learn the material; present
the material in class; and write an expository paper explaining the
material. Further details will be discussed in class.
Students will also be expected to actively participate
in class by asking and answering questions, making comments, etc.
Prerequisites:
Students should be familiar with basic probability theory (including
conditional distributions), and with basic Markov chain theory. Some
familiarity with statistical sampling theory would be helpful.
See
background references,
project
ideas, and
my CFTP
Java applet.
This document is available at http://markov.utstat.toronto.edu/jeff/courses/sta4247-01a.html.