STA 4502S: Topics in Stochastic Processes (Winter 2018)

This course will focus on convergence rates and other mathematical properties of Markov chains on both discrete and general state spaces. Specific methods to be covered will include coupling, minorization conditions, spectral analysis, and more. Applications will be made to card shuffling and to MCMC algorithms.

Instructor: Professor Jeffrey S. Rosenthal, Department of Statistics, University of Toronto. Sidney Smith Hall, room 5022; phone (416) 978-4594; e-mail; web

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 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).

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