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.
If you are not a Statistics Dept graduate student, then
**permission of the instructor** is required to enroll.

**Time:** Mondays, 2:10 -- 4:00. (First class January 10,
last class April 4, no class Febrary 21 [Reading Week].)

**Place:** Astronomy & Astrophysics Building (AB), 50 St.
George Street, room **107**.

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

**Instructor:**
Professor Jeffrey S. Rosenthal,
Department of Statistics, University of Toronto.
Sidney Smith Hall, room 5016B; phone 416-978-4594;
e-mail jeff@math.toronto.edu; web
http://probability.ca/jeff/

**Computing: **
Students will be required to write computer programs for this course.
The default computer language 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 24, due Feb 14 at 2:10pm;
HW#2 assigned Mar 7, due Mar 28 at 2:10pm);
project 50%
(assigned Feb 14; due Apr 4 at 2:10pm).

**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 7,8,9 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.

- 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]