On the optimal Halton sequence

H. Chi, M. Mascagni and Tony Warnock ()

Mathematics and Computers in Simulation (MATCOM), 2005, vol. 70, issue 1, 9-21

Abstract: Quasi-Monte Carlo methods are a variant of ordinary Monte Carlo methods that employ highly uniform quasirandom numbers in place of Monte Carlo’s pseudorandom numbers. Clearly, the generation of appropriate high-quality quasirandom sequences is crucial to the success of quasi-Monte Carlo methods. The Halton sequence is one of the standard (along with (t,s)-sequences and lattice points) low-discrepancy sequences, and one of its important advantages is that the Halton sequence is easy to implement due to its definition via the radical inverse function. However, the original Halton sequence suffers from correlations between radical inverse functions with different bases used for different dimensions. These correlations result in poorly distributed two-dimensional projections. A standard solution to this phenomenon is to use a randomized (scrambled) version of the Halton sequence. An alternative approach to this is to find an optimal Halton sequence within a family of scrambled sequences. This paper presents a new algorithm for finding an optimal Halton sequence within a linear scrambling space. This optimal sequence is numerically tested and shown empirically to be far superior to the original. In addition, based on analysis and insight into the correlations between dimensions of the Halton sequence, we illustrate why our algorithm is efficient for breaking these correlations. An overview of various algorithms for constructing various optimal Halton sequences is also given.

Keywords: Quasi-Monte Carlo; Scrambling; Correlation; Optimal Halton sequence (search for similar items in EconPapers)
Date: 2005
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (8)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S037847540500087X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:70:y:2005:i:1:p:9-21

DOI: 10.1016/j.matcom.2005.03.004

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().