IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1106.3562.html
   My bibliography  Save this paper

Geometric Allocation Approach for Transition Kernel of Markov Chain

Author

Listed:
  • Hidemaro Suwa
  • Synge Todo

Abstract

We introduce a new geometric approach that constructs a transition kernel of Markov chain. Our method always minimizes the average rejection rate and even reduce it to zero in many relevant cases, which cannot be achieved by conventional methods, such as the Metropolis-Hastings algorithm or the heat bath algorithm (Gibbs sampler). Moreover, the geometric approach makes it possible to find not only a reversible but also an irreversible solution of rejection-free transition probabilities. This is the first versatile method that can construct an irreversible transition kernel in general cases. We demonstrate that the autocorrelation time (asymptotic variance) of the Potts model becomes more than 6 times as short as that by the conventional Metropolis-Hastings algorithm. Our algorithms are applicable to almost all kinds of Markov chain Monte Carlo methods and will improve the efficiency.

Suggested Citation

  • Hidemaro Suwa & Synge Todo, 2011. "Geometric Allocation Approach for Transition Kernel of Markov Chain," Papers 1106.3562, arXiv.org, revised Jul 2012.
    • Handle: RePEc:arx:papers:1106.3562
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1106.3562
    File Function: Latest version
    Download Restriction: no
    ---><---

    Citations

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


    Cited by:

    1. Suwa, Hidemaro, 2024. "Reducing rejection exponentially improves Markov chain Monte Carlo sampling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:1106.3562. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.