IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v118y2008i12p2198-2222.html
   My bibliography  Save this article

Optimal acceptance rates for Metropolis algorithms: Moving beyond 0.234

Author

Listed:
  • Bédard, Mylène

Abstract

Recent optimal scaling theory has produced a condition for the asymptotically optimal acceptance rate of Metropolis algorithms to be the well-known 0.234 when applied to certain multi-dimensional target distributions. These d-dimensional target distributions are formed of independent components, each of which is scaled according to its own function of d. We show that when the condition is not met the limiting process of the algorithm is altered, yielding an asymptotically optimal acceptance rate which might drastically differ from the usual 0.234. Specifically, we prove that as d-->[infinity] the sequence of stochastic processes formed by say the i*th component of each Markov chain usually converges to a Langevin diffusion process with a new speed measure [upsilon], except in particular cases where it converges to a one-dimensional Metropolis algorithm with acceptance rule [alpha]*. We also discuss the use of inhomogeneous proposals, which might prove to be essential in specific cases.

Suggested Citation

  • Bédard, Mylène, 2008. "Optimal acceptance rates for Metropolis algorithms: Moving beyond 0.234," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2198-2222, December.
    • Handle: RePEc:eee:spapps:v:118:y:2008:i:12:p:2198-2222
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(07)00217-7
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

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

    References listed on IDEAS

    as
    1. Breyer, L. A. & Roberts, G. O., 2000. "From metropolis to diffusions: Gibbs states and optimal scaling," Stochastic Processes and their Applications, Elsevier, vol. 90(2), pages 181-206, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. O. F. Christensen & J. Møller & R. P. Waagepetersen, 2001. "Geometric Ergodicity of Metropolis-Hastings Algorithms for Conditional Simulation in Generalized Linear Mixed Models," Methodology and Computing in Applied Probability, Springer, vol. 3(3), pages 309-327, September.
    2. Peter Neal & Gareth Roberts, 2011. "Optimal Scaling of Random Walk Metropolis Algorithms with Non-Gaussian Proposals," Methodology and Computing in Applied Probability, Springer, vol. 13(3), pages 583-601, September.
    3. Peter Neal & Gareth Roberts, 2008. "Optimal Scaling for Random Walk Metropolis on Spherically Constrained Target Densities," Methodology and Computing in Applied Probability, Springer, vol. 10(2), pages 277-297, June.
    4. Yang, Jun & Roberts, Gareth O. & Rosenthal, Jeffrey S., 2020. "Optimal scaling of random-walk metropolis algorithms on general target distributions," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 6094-6132.
    5. Kamatani, Kengo, 2020. "Random walk Metropolis algorithm in high dimension with non-Gaussian target distributions," Stochastic Processes and their Applications, Elsevier, vol. 130(1), pages 297-327.
    6. Zanella, Giacomo & Bédard, Mylène & Kendall, Wilfrid S., 2017. "A Dirichlet form approach to MCMC optimal scaling," Stochastic Processes and their Applications, Elsevier, vol. 127(12), pages 4053-4082.

    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:eee:spapps:v:118:y:2008:i:12:p:2198-2222. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.