IDEAS home Printed from https://ideas.repec.org/a/bpj/mcmeap/v10y2004i3-4p435-442n25.html
   My bibliography  Save this article

On the Scrambled Halton Sequence

Author

Listed:
  • Mascagni Michael

    (Department of Computer Science and School of Computational Science and Information Technology, Florida State University, Tallahassee, FL 32306-4530, USA, E-mail: E-mail: , URL: http://www.cs.fsu.edu/∼mascagni Michael.Mascagni@fsu.edu)

  • Chi Hongmei

    (Department of Computer Science, Florida State University, Tallahassee, FL 32306-4120, USA, Email: chi@cs.fsu.edu)

Abstract

The Halton sequence is one of the standard (along with (t, s)-sequences and lattice points) low-discrepancy sequences, and thus is widely used in quasi-Monte Carlo applications. 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 is to use a randomized (scrambled) version of the Halton sequence. Here, we analyze the correlations in the standard Halton sequence, and based on this analysis propose a new and simpler modified scrambling algorithm. We also provide a number theoretic criterion to choose the optimal scrambling from among a large family of random scramblings. Based on this criterion, we have found the optimal scrambling for up to 60 dimensions for the Halton sequence. This derandomized Halton sequence is then numerically tested and shown empirically to be far superior to the original sequence.

Suggested Citation

  • Mascagni Michael & Chi Hongmei, 2004. "On the Scrambled Halton Sequence," Monte Carlo Methods and Applications, De Gruyter, vol. 10(3-4), pages 435-442, December.
    • Handle: RePEc:bpj:mcmeap:v:10:y:2004:i:3-4:p:435-442:n:25
    DOI: 10.1515/mcma.2004.10.3-4.435
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/mcma.2004.10.3-4.435
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/mcma.2004.10.3-4.435?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Chi, H. & Mascagni, M. & Warnock, T., 2005. "On the optimal Halton sequence," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 70(1), pages 9-21.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bpj:mcmeap:v:10:y:2004:i:3-4:p:435-442:n:25. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.