**Instructor:**
Professor Jeffrey S. Rosenthal,
Department of Statistics, University of Toronto.
Sidney Smith Hall, room 5022; phone (416) 978-4594;
e-mail
j.rosenthal@math.toronto.edu;
web
http://probability.ca/jeff/

**Lectures:** Wednesdays, 11:10 a.m. - 1:00 p.m.,
in room 2120 of Sidney Smith Hall
(building "SS" on campus map).
First class Feb 28. Last class April 4.

**Note:**
This is a **six-week class**, and only counts for 0.25 course credit.
The add/drop date is the day of the second lecture, i.e. March 7.

**Course Web Page:** Visit
probability.ca/sta4502
for course information and announcements.

**Prerequisites: **
Graduate-level probability theory with measure theory at the level of
STA2111,
and stochastic processes at the level of
STA447/2006 (may be concurrent).
Some linear algebra and group theory will also be used.
This course is intended primarily for graduate students in statistics;
all others must obtain **permission from the instructor**
before enroling.

**Evaluation (details below):**

35% class participation (all six classes)

20% providing detailed lecture notes for one class (as scheduled)

35% project *or* homework (due April 4 at 11:10 sharp; choose by March 21)

10% presentation (on April 4 in class)

For **class participation**, students are expected to
punctually attend class each week, to pay close attention during class
[no cell phones or laptops except for direct class-related purposes
with prior permission], answer questions posed by the instructor, ask
their own questions, review the previous material and notes before each
new lecture, and show interest and enthusiasm in the course material.

For **lecture notes**, each student will be assigned one
lecture, for which they
should prepare *detailed* notes which organise and
explain the material as clearly as possible, including providing
additional background information as needed. The notes should be
e-mailed to the instructor (hopefully in both pdf and LaTeX format)
by noon on the Monday following the class.

week 1 (Mufan);
week 2 (Louis);
week 3 (Joseph);
week 4 (Tiantian);
week 5 (Jeffrey).

For the **project**, students should choose an
interesting substantial example of a Markov chain which
converges to stationarity (e.g. from MCMC), and bound its
convergence time k_* as best as they can (perhaps in multiple different ways),
and write up a substantial report clearly explaining their Markov
chain and bounds in detail.
(It might be possible for two students to work jointly on a larger
project with prior permission -- contact the instructor if interested.)

Alternatively, for the **homework**, students should
solve in detail, with full explanation, all 14 of the problems at the
end of the
first review
paper older version, and write them up clearly and neatly.
(Note: each student should choose either the project
**or** the homework, and should inform the instructor of
their choice in class on March 21.)

The **presentations** will take place in the final class
on April 4, and will be a maximum of 16 minutes each, and should
either summarise your project (if you chose to do one),
or present the ideas behind your
solutions to a few interesting homework problems (Note: claim
your problems early, to avoid duplication with other presentations).

**Instructor Office Hours:**
You are welcome to talk to the instructor after class, or any time you
find him in his office, or you can e-mail him to arrange another time
to meet.

**Readings:**
There is no required textbook.
For an idea of the content of the course, see
this paper
/ older version
(discrete case) and
this paper
and this paper
and Section 2 of
this paper
(general case).

This document is available at probability.ca/sta4502, or permanently at probability.ca/jeff/teaching/1718/sta4502/