IDEAS home Printed from https://ideas.repec.org/a/taf/jnlasa/v119y2024i545p690-700.html
   My bibliography  Save this article

Stochastic Convergence Rates and Applications of Adaptive Quadrature in Bayesian Inference

Author

Listed:
  • Blair Bilodeau
  • Alex Stringer
  • Yanbo Tang

Abstract

We provide the first stochastic convergence rates for a family of adaptive quadrature rules used to normalize the posterior distribution in Bayesian models. Our results apply to the uniform relative error in the approximate posterior density, the coverage probabilities of approximate credible sets, and approximate moments and quantiles, therefore, guaranteeing fast asymptotic convergence of approximate summary statistics used in practice. The family of quadrature rules includes adaptive Gauss-Hermite quadrature, and we apply this rule in two challenging low-dimensional examples. Further, we demonstrate how adaptive quadrature can be used as a crucial component of a modern approximate Bayesian inference procedure for high-dimensional additive models. The method is implemented and made publicly available in the aghq package for the R language, available on CRAN. Supplementary materials for this article are available online.

Suggested Citation

  • Blair Bilodeau & Alex Stringer & Yanbo Tang, 2024. "Stochastic Convergence Rates and Applications of Adaptive Quadrature in Bayesian Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 119(545), pages 690-700, January.
    • Handle: RePEc:taf:jnlasa:v:119:y:2024:i:545:p:690-700
    DOI: 10.1080/01621459.2022.2141635
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/01621459.2022.2141635
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/01621459.2022.2141635?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:jnlasa:v:119:y:2024:i:545:p:690-700. 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/UASA20 .

    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.