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 methods. The course will involve a combination of methodological considerations, mathematical analysis, and computer programming.

**Prerequisite:** This course is designed for graduate
students in the Department of Statistics. All others should e-mail the instructor for permission to
enrol, which will only be granted if you have significant background
in statistics and probability. Some familiarity with basic computer
programming (e.g. if statements, for loops, etc.) is also required.

**Time:** Mondays, 2-4. (First class January 5, last class
April 6, no class Febrary 16 [Reading Week].)

**Place:** Bahen Centre, room 2145.
(Building "BA" on campus map.)

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

**References:**
There is no required textbook, but much of the material to be covered is
discussed in various sources, including:

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

**Instructor:**
Professor Jeffrey S. Rosenthal,
Department of Statistics, University of Toronto.
Sidney Smith Hall, room 6024; 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 including C and Java,
and some other languages will be accepted as substitutes on the homework
assignments.

**Evaluation:**

Item: |
Worth: |
Assigned by: |
Due (in class, by 2:10 sharp): |

HW#1 | 10% | Jan 19 | Feb 2 |

HW#2 | 12% | Feb 2 | Mar 2 |

HW#3 | 13% | Mar 2 | Mar 23 |

In-Class Test | 30% | N/A | Mar 30 (90 mins) |

Final Project | 35% | Jan 19 | April 6 |