STA 3431F: Monte Carlo Methods (Fall 2020; online synchronous)

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. (It will be similar to last year's course, though with some differences.)

See the evolving lecture notes and supplementary files, to be updated after each class (and you should review/try them before the next class).

Course Web Page: http://probability.ca/sta3431

Prerequisites: Knowledge of statistical inference and probability theory and basic Markov chains at the advanced undergraduate level (e.g. skim this book especially the Appendix), and familiarity with basic computer programming techniques (including "R", which you should review on your own if you have not previously used; see e.g. this page).

Instructor: Professor Jeffrey S. Rosenthal, Department of Statistics, University of Toronto. Email j.rosenthal@math.toronto.edu; web http://probability.ca/jeff/

Who May Take This Course? This course is intended primarily for Statistics Department graduate students. Graduate students from other UofT departments must request permission from the instructor (by Sept 10 at the latest) to enrol; email me about your course interest and program and prerequisites including all your university transcripts, and then if I agree then you are responsible for sorting out any necessary forms/paperwork (which I will sign by email where required). Unfortunately, undergraduate/auditing students may not take this class, though you are still welcome to work through the course materials on this web site on your own.

Lectures: Mondays, 10:10 a.m. - 12:00 noon (Toronto time), online (on Zoom; synchronous only). First class Sept 14. Last class Dec 7. No class Oct 12 (Thanksgiving) nor Nov 9 (Reading Week). Lectures will be interactive; please put away your cell phones and pay close attention to the material being presented.

Zoom information: All lectures will given live (synchronous) over Zoom. They will not be recorded. Here is some information about using Zoom in this class:

  1. The Zoom link will be emailed to all enrolled students before the first class. That same link will work for all the classes (and also for any office hours, etc). Please save and bookmark it. However, please do not post it publicly, to avoid zoom-bombers. (If you have not received the Zoom link by now, then please email the instructor to receive it.)
  2. You should connect on Zoom before the class start time of 10:10, hopefully between 10:00 and 10:05.
  3. Please connect from a quiet room, where you can be alone without any distractions.
  4. If possible, use a laptop or desktop computer, not an iPad or cell phone -- and the actual Zoom app, not the web browser version -- for best funcationality and viewing.
  5. Please leave your computer's camera on, so we can all see each other.
  6. Optionally, you may wish to mute your microphone when you are not speaking, to prevent any background noises from disrupting the class.
  7. If necessary, use "Rename" on Zoom to make it display your usual first and last name (but not student number).
  8. You should pay close attention during class, and refrain from sending or reading any private messages, emails, Facebook posts, etc.
  9. During class, the instructor will use "share screen" to display his lecture notes and computer simulations. You should be able to see both the instructor and the screen he is sharing. All of the notes and computer programs will later be posted on this web page.

Instructor Office Hours: You are welcome to talk to the instructor on Zoom after class, or you can email your questions to him, or you can email him to arrange a time to talk on Zoom. There will be special STA3431 office hours/meetings on Thurs Oct 1 at 11:45 on Gather Town, and Tues Oct 6 at 11:30 on Zoom. I will set up additional specific office hours/meetings later.

Discussion Page: I created a general STA3431 Discussion Page on the course's quercus page, where students can post comments and questions about the course. Feel free to post course-related messages there any time you want to. I may or may not read your posts myself, but other students can answer them whenever they wish. Also, a student has created a STA3431 discord page. You may also wish to form a study group or join a drop-in study space.

Evaluation:
20% Class participation (your attendance / punctuality / preparation / attention / responses during lectures)
25% Homework #1 (due Thurs Oct 8 at 1:00 pm sharp; upload to Quercus one separate pdf file for each question)
25% Homework #2 (due Fri Nov 6 at 1:00 pm sharp)
25% Final Project (due Fri Nov 27 at 1:00 pm sharp)
5% Brief Presentation (about your project, in class on Nov 30 or Dec 7)

Lateness policy: Homeworks are due sharply at the designated 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 emailing the instructor a complete explanation of your concern (together with your full name, student number, e-mail address, and telephone number), 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.

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]

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 or Navi for assistance and support.



This document is available at probability.ca/sta3431, or permanently at probability.ca/jeff/teaching/2021/sta3431/