The acceptance-rejection method for low-discrepancy sequences

Nguyen Nguyet () and Ökten Giray ()
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Nguyen Nguyet: Department of Mathematics and Statistics, Youngstown State University, Youngstown, OH 44555-7994, USA
Ökten Giray: Department of Mathematics, Florida State University, Tallahassee FL 32306-4510, USA

Monte Carlo Methods and Applications, 2016, vol. 22, issue 2, 133-148

Abstract: Generation of pseudorandom numbers from different probability distributions has been studied extensively in the Monte Carlo simulation literature. Two standard generation techniques are the acceptance-rejection and inverse transformation methods. An alternative approach to Monte Carlo simulation is the quasi-Monte Carlo method, which uses low-discrepancy sequences, instead of pseudorandom numbers, in simulation. Low-discrepancy sequences from different distributions can be obtained by the inverse transformation method, just like for pseudorandom numbers. In this paper, we present an acceptance-rejection algorithm for low-discrepancy sequences. We prove a convergence result, and present error bounds. We then use this acceptance-rejection algorithm to develop quasi-Monte Carlo versions of some well-known algorithms to generate beta and gamma distributions, and investigate the efficiency of these algorithms numerically. We also consider the simulation of the variance gamma model, a model used in computational finance, where the generation of these probability distributions are needed. Our results show that the acceptance-rejection technique can result in significant improvements in computing time over the inverse transformation method in the context of low-discrepancy sequences.

Keywords: Acceptance-rejection method; low-discrepancy sequences; quasi-Monte Carlo; beta distribution; gamma distribution; variance gamma model (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1515/mcma-2016-0104

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