STA4502: Monte Carlo Estimation (Jan-Feb 2013)

[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;; 'jeff' at ''

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 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.

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 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:

Certain on-line materials might also be useful, including: In addition, the following book chapters might be helpful:

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