[See also the evolving lecture notes and supplementary files.]This course will explore Monte Carlo algorithms, which use randomness to estimate difficult high-dimensional quantities. Topics will include Monte Carlo integration, the rejection sampler, importance sampling, and Markov chain Monte Carlo (MCMC) methods such as the Metropolis algorithm, the Metropolis-Hastings algorithm, variable-at-a-time MCMC, tempered MCMC, and simulated annealing. As time permits, it might also include transdimensional MCMC, applications of MCMC to Bayesian inference and financial modeling, theoretical justification and analysis of MCMC algorithms, and adaptive MCMC techniques. The course will involve a combination of methodological considerations, mathematical analysis, and computer programming.

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

**Time:** Wednesdays 11:10 - 1:00, and Fridays 11:10 - 12:00.
First class Jan 9. Last class Feb 15.

**Location:**
Room 1200 of the Bahen Centre
(building "BA" on campus map).

**Note:** This course lasts only **six
weeks**, and counts for only a **quarter credit**.
(It may be combined with e.g. the follow-up six-week course STA4503
by Professor Radford
Neal to together equal a usual half-course credit.)

**Last Date to Enrol in [Add] this Course:** Tuesday
Jan 15.

**Last Date to Drop this Course:** Friday Jan 25.

**Course Web Page:** Visit
probability.ca/sta4502
for course information and materials.

**Prerequisites: **
Knowledge of statistical inference and probability theory at the
advanced undergraduate level, and familiarity with **basic**
computer programming techniques.
**Students other than Stat Dept graduate students should e-mail
the instructor to request permission to enrol.**

**Evaluation:**

Class participation, 10%;

Homework assignment, due on Fri Feb 8 at 11:10 sharp, 50%;

Course project, officially due on Fri Feb 15, 40%.

**Computing: ** Students will be required to
write computer programs for this course. The default computer
language is "R", which is freely available and is designed for
statistical computation (more information is available at probability.ca/Rinfo.html). 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 assignments.

**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 on-line). The book closest to this course is probably:

- Chapters 7,8,9 of Robert Gray's on-line notes.
- Chapters 4,5,6,7 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]

This document is available at www.probability.ca/sta4502 or permanently at www.probability.ca/jeff/teaching/1213/sta4502/