STA 3431F: Monte Carlo Methods (Fall 2019)

This course will explore Monte Carlo computer algorithms, which use randomness to perform difficult high-dimensional computations. Different types of algorithms, theoretical issues, and practical applications will all be considered. Particular emphasis will be placed on Markov chain Monte Carlo (MCMC) methods. The course will involve a combination of methodological investigations, mathematical analysis, and computer programming.

See also the evolving lecture notes and supplementary files, to be updated after each lecture.

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

Lectures: Mondays, 10:10 a.m. - 12:00 noon, OISE (OI) room 5150. First class Sept 9. Last class Dec 2. No class Oct 14 (Thanksgiving) or Nov 4 (Reading Week). During lectures, please put away your laptops and cell phones (unless you are using them specifically for a class-related purpose with prior permission), and pay attention to the material being presented.

Course Web Page: Visit for course information and announcements.

Prerequisites: Knowledge of statistical inference and probability theory and basic Markov chains at the advanced undergraduate level, and familiarity with basic computer programming techniques (including "R"). This course is intended primarily for Statistics Department graduate students; all others must request permission from the instructor (by Sept 18 at the latest) to enrol (best is to provide background information about your prerequisites including transcript(s), and then present me with any necessary forms right after the first class).

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 any time to arrange another time to meet. Special office hours in SS 5022 on: Friday Oct 18 from 2:30 to 4:00. Friday Nov 15 from 3:30 to 4:30. Wednesday Nov 20 from 4:30 to 5:30.

Supplementary Reading: There is no required textbook, but much of the material to be covered is discussed in various sources. The book closest to this course is probably:
*** C.P. Robert and G. Casella (2005), Monte Carlo Statistical Methods. [library / amazon]
Certain on-line materials might also be useful, including:
*** Chapters 7,8,9 of Robert Gray's on-line notes.
*** Chapters 4,5,6 of Galin Jones' on-line notes.
*** Chapter 2 of Gareth Roberts' on-line notes.
In addition, the following book chapters might be helpful:
*** Chapters 2,5,6 of J.S. Liu (2001), Monte Carlo Strategies in Scientific Computing. [library / online / amazon]
*** Chapters 6,7,8 of G.H. Givens and J.A. Hoeting (2005), Computational Statistics. [library / amazon ]
*** Chapters 10,11,12,13 of J.F. Monahan (2001), Numerical Methods of Statistics. [library / amazon]

5% Class attendance / punctuality / preparation / attention / participation
20% Homework #1 (assigned by Sept 23, due Oct 21 at 10:10 a.m. sharp)
30% Homework #2 including Mini-Project (assigned by Oct 28, due Nov 25 at 10:10 a.m. sharp)
40% Test (Nov 18, in class; 100 minutes)
5% Presentation (Nov 25 and Dec 2; five minutes each)

Lateness policy: Homeworks are due sharply at the appointed time, and will receive significant penalties if they are late.

Regrading policy: Regrading requests should only be made for genuine grading errors, and should be initiated by writing or typing a complete explanation of your concern (together with your full name, student number, e-mail address, and telephone number) on a separate piece of paper, and giving this together with your original unaltered homework/test paper to the instructor within one week of when the graded item was first available. Warning: your mark may end up going down rather than up. More details are here.

Challenges? If you encounter challenges during your studies, then please visit Academic Success or the Health and Wellness Centre or Graduate Wellness Services or the SGS Wellness Portal for assistance and support.

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