IDEAS home Printed from https://ideas.repec.org/a/bla/jorssb/v60y1998i1p255-268.html
   My bibliography  Save this article

Optimal scaling of discrete approximations to Langevin diffusions

Author

Listed:
  • Gareth O. Roberts
  • Jeffrey S. Rosenthal

Abstract

We consider the optimal scaling problem for proposal distributions in Hastings–Metropolis algorithms derived from Langevin diffusions. We prove an asymptotic diffusion limit theorem and show that the relative efficiency of the algorithm can be characterized by its overall acceptance rate, independently of the target distribution. The asymptotically optimal acceptance rate is 0.574. We show that, as a function of dimension n, the complexity of the algorithm is O(n1/3), which compares favourably with the O(n) complexity of random walk Metropolis algorithms. We illustrate this comparison with some example simulations.

Suggested Citation

  • Gareth O. Roberts & Jeffrey S. Rosenthal, 1998. "Optimal scaling of discrete approximations to Langevin diffusions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(1), pages 255-268.
    • Handle: RePEc:bla:jorssb:v:60:y:1998:i:1:p:255-268
    DOI: 10.1111/1467-9868.00123
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/1467-9868.00123
    Download Restriction: no
    File URL: https://libkey.io/10.1111/1467-9868.00123?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
    ---><---

    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:bla:jorssb:v:60:y:1998:i:1:p:255-268. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/rssssea.html .

    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.