Randomized Quasi-Monte Carlo: An Introduction for Practitioners

Pierre L'Ecuyer (1, 2)

1 DIONYSOS - Dependability Interoperability and perfOrmance aNalYsiS Of networkS
2 DIRO - Département d'Informatique et de Recherche Opérationnelle [Montreal]

We survey basic ideas and results on randomized quasi-Monte Carlo (RQMC) methods, discuss their practical aspects, and give numerical illustrations. RQMC can improve accuracy compared with standard Monte Carlo (MC) when estimating an integral interpreted as a mathematical expectation. RQMC estimators are unbiased and their variance converges at a faster rate (under certain conditions) than MC estimators, as a function of the sample size. Variants of RQMC also work for the simulation of Markov chains, for function approximation and optimization, for solving partial differential equations, etc. In this introductory survey, we look at how RQMC point sets and sequences are constructed, how we measure their uniformity, why they can work for high-dimensional integrals, and how can they work when simulating Markov chains over a large number of steps.

Domains: Operations Research [math.OC]

Pierre L'Ecuyer. Randomized Quasi-Monte Carlo: An Introduction for Practitioners. 12th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (MCQMC 2016), Aug 2016, Stanford, United States. ⟨hal-01561550⟩