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

**Prerequisite:**
Knowledge of statistical inference and probability theory at the
advanced undergraduate level, and familiarity with basic computer
programming techniques.

**Time:** Mondays, 2-4. (First class January 4, last class
March 30, no class Febrary 15 [Reading Week].)

**Place:** Lash Miller Chemical Labs (LM), room 123.

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

**Instructor:**
Professor Jeffrey S. Rosenthal,
Department of Statistics, University of Toronto.
Sidney Smith Hall, room 5016B; phone (416) 978-4594;
http://probability.ca/jeff/;

**Computing: **
Students will be required to write computer programs for this course.
The default computer language (**required** for
the in-class test) will be "R", which is freely available and is
designed for statistical computation (more information is available
here). However, the instructor may also
present some examples in other computer languages (e.g. C, Java),
and some other languages may (with prior permission)
be accepted on the homework assignments.

**Evaluation:**
Homeworks 50% (HW#1 assigned Jan 18, due Feb 8;
HW#2 assigned Mar 1, due Mar 22);
Project 50% (due Mar 29).

**References:**
There is no required textbook, but much of the material to be covered is
discussed in various sources (plus the instructor will provide rough
lecture notes). The book closest to this course is probably:

- Chapters 7-9 of Robert Gray's on-line notes.
- Chapters 4-6 of Galin Jones' on-line notes.
- Chapter 2 of Gareth Roberts' on-line notes.

- Chapters 2, 5, and 6 of J.S. Liu (2001), Monte Carlo Strategies in Scientific Computing. [library / online / amazon]
- Chapters 6-8 of G.H. Givens and J.A. Hoeting (2005), Computational Statistics. Wiley. [library / amazon ]
- Chapter 10-13 of J.F. Monahan (2001), Numerical Methods of Statistics. Cambridge University Press. [library / amazon]