IDEAS home Printed from https://ideas.repec.org/a/taf/amstat/v78y2024i3p290-296.html
   My bibliography  Save this article

A Note on Monte Carlo Integration in High Dimensions

Author

Listed:
  • Yanbo Tang

Abstract

Monte Carlo integration is a commonly used technique to compute intractable integrals and is typically thought to perform poorly for very high-dimensional integrals. To show that this is not always the case, we examine Monte Carlo integration using techniques from the high-dimensional statistics literature by allowing the dimension of the integral to increase. In doing so, we derive nonasymptotic bounds for the relative and absolute error of the approximation for some general classes of functions through concentration inequalities. We provide concrete examples in which the magnitude of the number of points sampled needed to guarantee a consistent estimate varies between polynomial to exponential, and show that in theory arbitrarily fast or slow rates are possible. This demonstrates that the behavior of Monte Carlo integration in high dimensions is not uniform. Through our methods we also obtain nonasymptotic confidence intervals which are valid regardless of the number of points sampled.

Suggested Citation

  • Yanbo Tang, 2024. "A Note on Monte Carlo Integration in High Dimensions," The American Statistician, Taylor & Francis Journals, vol. 78(3), pages 290-296, July.
    • Handle: RePEc:taf:amstat:v:78:y:2024:i:3:p:290-296
    DOI: 10.1080/00031305.2023.2267637
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/00031305.2023.2267637
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/00031305.2023.2267637?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.

    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:taf:amstat:v:78:y:2024:i:3:p:290-296. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/UTAS20 .

    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.