Applied Mathematics Colloquia by Art Owen: Recent Progress in Error Estimation for Quasi-Monte Carlo

Speaker:

Art Owen, professor of statistics, Stanford University

Title:

Recent Progress in Error Estimation for Quasi-Monte Carlo

Abstract:

For many high dimensional integration problems, Quasi Monte Carlo methods attain the best accuracy. In settings where high accuracy is required it is also valuable to show that it has been attained. Those two criteria are somewhat at odds with each other.  This talk looks at recent ways to quantify the accuracy attained by QMC.  It includes progress in forming confidence intervals based on replication of randomized QMC.  The surprise there is that a plain student's t based confidence interval method proved to be much more reliable than some bootstrap methods that were expected to be best. A second area of recent progress provides computable and provable upper and lower bounds on the integral. These methods require special QMC points that have a non-negative local discrepancy property along with an integrand that has a complete monotonicity property.  At present, some of the best QMC accuracy results arise for a median of means strategy. That raises a severe open challenge of quantifying the uncertainty in a mean when one has computed a median.

This talk includes joint work with Michael Gnewuch, Peter Kritzer, Zexin Pan, Pierre L'Ecuyer, Marvin Nakayama and Bruno Tuffin.

Applied Mathematics Colloquia