In connection with the 1998-1999 Probability and Its Applications Program, the following course is offered for graduate students and interested faculty members. Its aim is to provide mathematicians possessing the appropriate background with an opportunity to learn more detail about some of the topics that will be featured prominently in the program seminars and workshops.

This course examines Monte Carlo methods for computer simulations. Theoretical properties are studied as well as practical issues concerning computer implementation and statistical analysis.

Topics include:

" Computer-generated random numbers
" Monte Carlo integration
" Markov chain Monte Carlo
" Statistical analysis of output data
" Efficiency considerations

" Applications in statistical physics (percolation, self-avoiding walk, Ising model)
" Applications in Bayesian statistics
" Applications in communications networks
" Aimulated annealing
" Other applications

Prerequisite: An undergraduate course in probability.

Instructor: Neal Madras, Department of Mathematics and Statistics, York University

Evaluation (for graduate students taking the course for credit):

Homework (about 6 problem sets): 50%
Project: 20%
Final exam (take-home): 30%

Time: (starting September 7, 1998)

Credit: As graduate students at any of Fields sponsoring or affiliate universities, you may discuss the possibility of credit for this lecture series with your home university graduate officer and the course instructor. Assigned reading and related projects may be arranged for the benefit of students requiring these courses for credit.

References and suggested reading:

Binder and Heermann (1992), "Monte Carlo Simulation in Statistical Physics" (Springer)
Bratley, Fox, and Schrage (1987), "A Guide to Simulation" (Springer)
Devroye (1986), "Non-uniform Random Variate Generation" (Springer)
Frenkel and Smit (1996), "Understanding Molecular Simulation" (Academic)
Gilks, Richardson, and Spiegelhalter (1996): "Markov Chain MonteCarlo in Practice" (Chapman and Hall)
Madras and Slade (1993), "The Self-Avoiding Walk" (Birkhauser)