Description:

Fred Hickernell

IIT

Title: Reliable Error Estimation for Monte Carlo and Quasi-Monte Carlo Simulation

Abstract: When performing a simulation it is natural to wonder what the error is and how many runs are required to achieve a desired accuracy. Popular error estimates are based on large sample results, such as the Central Limit Theorem, or heuristics, but these error estimates can be fooled. We explain how these popular estimates can fail and present new, guaranteed, data-based error bounds for (quasi-)Monte Carlo simulation. These error bounds can be used to construct “black-box” adaptive simulation algorithms that stop when the accuracy requirement is met. Moreover, we provide upper bounds on the costs of these adaptive algorithms that show a reasonable dependence on the unknown difficulty of the problem.

Bio: Fred J. Hickernell enjoys problems that lie at the intersection of computational mathematics and statistics. These problems include (quasi-)Monte Carlo simulation, experimental design, kriging (a.k.a. mesh free approximation), and the tractability of high dimensional problems. He received his PhD in applied mathematics from Massachusetts Institute of Technology and previously taught at the University of Southern California and Hong Kong Baptist University. In 2005 Fred moved to Chicagoland where he serves as Professor and Chair of the Department of Applied Mathematics at Illinois Institute of Technology. Fred is a Fellow of the Institute of Mathematical Statistics and serves on the editorial boards of several computational mathematics journals.