This course will discuss recent advances in Markov Chain Monte Carlo algorithms. Topics covered will include the use of auxiliary variables, as in the Swendson-Wang algorithm and slice sampling; sampling methods based on Langevin and Hamiltonian dynamics; methods for handling isolated modes by annealing or tempering; methods for computing normalizing constants, such as the acceptance ratio method, umbrella sampling, and annealed importance sampling; and recent work on exact sampling with Markov chains by coupling from the past. Software will be provided to allow students to try applying many of these methods to Bayesian inference and other problems.
The basics of Markov chain Monte Carlo will be reviewed at the start, but students should preferably have some previous exposure to Monte Carlo methods, such as would be obtained by having taken STA 3431 in previous years, or the course on Monte Carlo methods offered at the Fields Institute in Fall 1998. Graduate students may be able to take this Fields Institute course for credit. For more details, see http://www.fields.utoronto.ca/graduate_courses.html.