Quasi-Monte Carlo methods for high dimensional integration

Speaker: Dr Frances Kuo
School of Mathematics, UNSW

Time: 4:00p.m. Wednesday 28th July 2004

Venue: Red Centre Room RC-4082
near Barker Street Gate 14

Abstract:

High dimensional integrals occur in a variety of areas such as quantum
mechanics, statistics and mathematical finance. In this day and age there is
a strong demand for methods to effectively and efficiently approximate
integrals in hundreds or even thousands of dimensions. The most well accepted
tools for handling such high dimensional problems are Monte Carlo methods,
which are equal-weight quadrature rules based on random sampling. Quasi-Monte
Carlo methods aim at offering a better alternative, with deterministically
chosen quadrature points tailored for numerical integration of specific
classes of functions. There have been tremendous advances in this area of
research during the past few years. This includes both the tractability
analysis, which provides insights on how to break the curse of
dimensionality, as well as profound constructive algorithms that bridge the
gulf between theory and practical application.

In this talk, I will introduce the two main families of quasi-Monte Carlo
methods: lattice rules and nets. You will learn how these methods are
constructed, how the approximation of the integral is obtained, how
randomization provides error estimation, and how the effective dimensions of
the problem are estimated.