Computational Mathematics and Statistics Seminar by Fred Hickernell: Low Discrepancy Drop-In Replacements for IID
Speaker: Fred Hickernell, professor of applied mathematics, Illinois Tech
Title: Low Discrepancy Drop-In Replacements for IID
Abstract: Low discrepancy (LD) sequences facilitate faster convergence for computing expectations or integrals of high dimensional functions. Unfortunately, the best low discrepancy sequences have preferred sample sizes, n, such as integer powers of 2. This may be inconvenient for practitioners who are accustomed to using independent and identically distributed (IID) samples that have no restrictions on n.
This talk describes recent work on lattice, Kronecker, and other LD sequences where the n may be any positive integer, and the dimension, d, is also allowed to be of arbitrary size. We use component-by-component constructions based on a figure of merit that includes the discrepancies for all values of n up to a maximum value, N. Because these discrepancies are based on carefully chosen kernels, the cost of the constructions is at most O(dNlog(N)).
Computational Mathematics and Statistics Seminar