IDEAS home Printed from https://ideas.repec.org/a/oup/biomet/v94y2007i4p787-807.html
   My bibliography  Save this article

Population-Based Reversible Jump Markov Chain Monte Carlo

Author

Listed:
  • Ajay Jasra
  • David A. Stephens
  • Christopher C. Holmes

Abstract

We present an extension of population-based Markov chain Monte Carlo to the transdimensional case. A major challenge is that of simulating from high- and transdimensional target measures. In such cases, Markov chain Monte Carlo methods may not adequately traverse the support of the target; the simulation results will be unreliable. We develop population methods to deal with such problems, and give a result proving the uniform ergodicity of these population algorithms, under mild assumptions. This result is used to demonstrate the superiority, in terms of convergence rate, of a population transition kernel over a reversible jump sampler for a Bayesian variable selection problem. We also give an example of a population algorithm for a Bayesian multivariate mixture model with an unknown number of components. This is applied to gene expression data of 1000 data points in six dimensions and it is demonstrated that our algorithm outperforms some competing Markov chain samplers. In this example, we show how to combine the methods of parallel chains (Geyer, 1991), tempering (Geyer & Thompson, 1995), snooker algorithms (Gilks et al., 1994), constrained sampling and delayed rejection (Green & Mira, 2001). Copyright 2007, Oxford University Press.

Suggested Citation

  • Ajay Jasra & David A. Stephens & Christopher C. Holmes, 2007. "Population-Based Reversible Jump Markov Chain Monte Carlo," Biometrika, Biometrika Trust, vol. 94(4), pages 787-807.
    • Handle: RePEc:oup:biomet:v:94:y:2007:i:4:p:787-807
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1093/biomet/asm069
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

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

    Citations

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


    Cited by:

    1. Lefebvre, Geneviève & Steele, Russell & Vandal, Alain C., 2010. "A path sampling identity for computing the Kullback-Leibler and J divergences," Computational Statistics & Data Analysis, Elsevier, vol. 54(7), pages 1719-1731, July.
    2. Enrico Petretto & Leonardo Bottolo & Sarah R Langley & Matthias Heinig & Chris McDermott-Roe & Rizwan Sarwar & Michal Pravenec & Norbert Hübner & Timothy J Aitman & Stuart A Cook & Sylvia Richardson, 2010. "New Insights into the Genetic Control of Gene Expression using a Bayesian Multi-tissue Approach," PLOS Computational Biology, Public Library of Science, vol. 6(4), pages 1-13, April.
    3. McGrory, C.A. & Pettitt, A.N. & Faddy, M.J., 2009. "A fully Bayesian approach to inference for Coxian phase-type distributions with covariate dependent mean," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4311-4321, October.
    4. William Astle & Maria De Iorio & Sylvia Richardson & David Stephens & Timothy Ebbels, 2012. "A Bayesian Model of NMR Spectra for the Deconvolution and Quantification of Metabolites in Complex Biological Mixtures," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1259-1271, December.
    5. Marco Di Zio & Ugo Guarnera, 2008. "A multiple imputation method for non-Gaussian data," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 75-90.
    6. Komárek, Arnost, 2009. "A new R package for Bayesian estimation of multivariate normal mixtures allowing for selection of the number of components and interval-censored data," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 3932-3947, October.
    7. Athanassios Petralias & Pródromos Prodromídis, 2015. "Price discovery under crisis: uncovering the determinant factors of prices using efficient Bayesian model selection methods," Empirical Economics, Springer, vol. 49(3), pages 859-879, November.
    8. Fabrizio Leisen & Roberto Casarin & David Luengo & Luca Martino, 2013. "Adaptive Sticky Generalized Metropolis," Working Papers 2013:19, Department of Economics, University of Venice "Ca' Foscari".
    9. Pandolfi, Silvia & Bartolucci, Francesco & Friel, Nial, 2014. "A generalized multiple-try version of the Reversible Jump algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 298-314.
    10. Li Ma, 2015. "Scalable Bayesian Model Averaging Through Local Information Propagation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 795-809, June.
    11. Spezia, Luigi, 2020. "Bayesian variable selection in non-homogeneous hidden Markov models through an evolutionary Monte Carlo method," Computational Statistics & Data Analysis, Elsevier, vol. 143(C).
    12. Rigat, F. & Mira, A., 2012. "Parallel hierarchical sampling: A general-purpose interacting Markov chains Monte Carlo algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1450-1467.
    13. Jasra, Ajay & Doucet, Arnaud & Stephens, David A. & Holmes, Christopher C., 2008. "Interacting sequential Monte Carlo samplers for trans-dimensional simulation," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1765-1791, January.

    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:oup:biomet:v:94:y:2007:i:4:p:787-807. 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: Oxford University Press (email available below). General contact details of provider: https://academic.oup.com/biomet .

    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.