MATH 288—Probability Topics

Mark Huber

MW 2:50-4:05 Physics 218

Monte Carlo methods for Numerical Integration

This will be a course on Monte Carlo methods, concentrating on Markov chain methods and perfect sampling techniques. Monte Carlo techniques for numerical integration have become an invaluable tool to statisticians, physicists, and computer scientists over the last few decades as the integration problems considered grow in dimension. The class is roughly 50/50 applications and theory. On the theory side, the focus is on provably efficient methods, that is, what theorems can be used effectively to show that various Markov chain methods actually work in a reasonable amount of time. Methods such as coupling and conductance will be introduced to show that Markov chains are rapidly mixing. Self-reducibility will then be utilized to give efficient methods for numerical integration.

Textbook: There is no textbook for this course, various survey papers and tutorials on topics will be given to the class to read.

Grading: Grades will be determined by weekly homework assignment, there will be no exams.

Prerequisites: There are no formal prerequisites, but a knowledge of probability at the undergraduate level will be expected. Measure theory is not a prerequisite for the course.