Quasi-Monte Carlo (QMC) for practical problems
QMC methods create statistical simulations of practical problems and generate estimates of a problem’s parameter distribution. Using highly uniform sampling mechanisms, QMC is intended to improve upon the random sampling inherent in classical Monte Carlo. Christiane Lemieux’s research involves creating QMC constructions, algorithms and software for use in a variety of situations and industries. “I like constructions that are flexible, that are not tuned to a particular problem but well suited to a class of problems,” says Christiane. “I develop constructions and software that I can safely recommend to people interested in QMC methods.”
QMC relies on computational mathematics. Christiane explains: “QMC deals with problems with no analytical solutions. Computational power is required to run QMC simulations, and also to construct uniformly distributed point sets (low-discrepancy sequences) in high-dimensional space. Constructions need to have nice structures. To get them, we rely on number theory, abstract algebra, and intensive computer searches.”
For Christiane, computational math and the CCMIC offer potential for variety and exposure to different influences. “I’m a multidisciplinary person. I like to understand the connections between different fields and my research,” she notes. “At CCMIC, everyone has different expertise, techniques and tools. It’s incredibly useful to see what others are doing and try to apply it to your own work.”
Christiane is currently working on using dependence concepts to provide new insights on QMC methods. She also plans to integrate to her QMC software the numerous additional features that she and her students have implemented over the last few years.