IDEAS home Printed from https://ideas.repec.org/a/bla/istatr/v89y2021i2p237-249.html
   My bibliography  Save this article

Rao–Blackwellisation in the Markov Chain Monte Carlo Era

Author

Listed:
  • Christian P. Robert
  • Gareth Roberts

Abstract

Rao–Blackwellisation is a notion often occurring in the MCMC literature, with possibly different meanings and connections with the original Rao–Blackwell theorem as established by C.R. Rao in 1945 and D. Blackwell in 1947, including a reduction of the variance of the resulting Monte Carlo approximations. This survey reviews some of the meanings of the term.

Suggested Citation

  • Christian P. Robert & Gareth Roberts, 2021. "Rao–Blackwellisation in the Markov Chain Monte Carlo Era," International Statistical Review, International Statistical Institute, vol. 89(2), pages 237-249, August.
    • Handle: RePEc:bla:istatr:v:89:y:2021:i:2:p:237-249
    DOI: 10.1111/insr.12463
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/insr.12463
    Download Restriction: no
    File URL: https://libkey.io/10.1111/insr.12463?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
    ---><---

    References listed on IDEAS

    as
    1. Pierre Del Moral & Arnaud Doucet & Ajay Jasra, 2006. "Sequential Monte Carlo samplers," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 411-436, June.
    2. A. Mira & J. Møller & G. O. Roberts, 2001. "Perfect slice samplers," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(3), pages 593-606.
    3. Alexandros Beskos & Omiros Papaspiliopoulos & Gareth O. Roberts & Paul Fearnhead, 2006. "Exact and computationally efficient likelihood‐based estimation for discretely observed diffusion processes (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 333-382, June.
    4. Jean-Marie Cornuet & Jean-Michel Marin & Antonietta Mira & Christian P. Robert, 2012. "Adaptive Multiple Importance Sampling," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(4), pages 798-812, December.
    5. Gareth O. Roberts & Jeffrey S. Rosenthal, 1999. "Convergence of Slice Sampler Markov Chains," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 643-660.
    6. repec:dau:papers:123456789/4644 is not listed on IDEAS
    7. Nicolas Chopin & Christian P. Robert, 2010. "Properties of nested sampling," Biometrika, Biometrika Trust, vol. 97(3), pages 741-755.
    8. repec:dau:papers:123456789/4645 is not listed on IDEAS
    9. repec:dau:papers:123456789/10690 is not listed on IDEAS
    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. Christian P. Robert, 2013. "Bayesian Computational Tools," Working Papers 2013-45, Center for Research in Economics and Statistics.
    2. Gael M. Martin & David T. Frazier & Christian P. Robert, 2020. "Computing Bayes: Bayesian Computation from 1763 to the 21st Century," Monash Econometrics and Business Statistics Working Papers 14/20, Monash University, Department of Econometrics and Business Statistics.
    3. Christophe Andrieu & Arnaud Doucet & Roman Holenstein, 2010. "Particle Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 269-342, June.
    4. Gareth W. Peters & Rodrigo S. Targino & Mario V. Wüthrich, 2017. "Bayesian Modelling, Monte Carlo Sampling and Capital Allocation of Insurance Risks," Risks, MDPI, vol. 5(4), pages 1-51, September.
    5. Matti Vihola & Jouni Helske & Jordan Franks, 2020. "Importance sampling type estimators based on approximate marginal Markov chain Monte Carlo," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1339-1376, December.
    6. Filippi Sarah & Barnes Chris P. & Cornebise Julien & Stumpf Michael P.H., 2013. "On optimality of kernels for approximate Bayesian computation using sequential Monte Carlo," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 12(1), pages 87-107, March.
    7. Nicolas Chopin & Alessandra Iacobucci & Jean-Michel Marin & Kerrie L. Mengersen & Christian P. Robert & Robin Ryder & Christian Schafer, 2010. "On Particle Learning," Working Papers 2010-22, Center for Research in Economics and Statistics.
    8. S. G. J. Senarathne & C. C. Drovandi & J. M. McGree, 2020. "Bayesian sequential design for Copula models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 454-478, June.
    9. Arnaud Dufays, 2016. "Evolutionary Sequential Monte Carlo Samplers for Change-Point Models," Econometrics, MDPI, vol. 4(1), pages 1-33, March.
    10. Johnson, Alicia A. & Jones, Galin L., 2015. "Geometric ergodicity of random scan Gibbs samplers for hierarchical one-way random effects models," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 325-342.
    11. Markussen, Bo, 2009. "Laplace approximation of transition densities posed as Brownian expectations," Stochastic Processes and their Applications, Elsevier, vol. 119(1), pages 208-231, January.
    12. Julie Lyng Forman & Michael Sørensen, 2008. "The Pearson Diffusions: A Class of Statistically Tractable Diffusion Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(3), pages 438-465, September.
    13. James Martin & Ajay Jasra & Emma McCoy, 2013. "Inference for a class of partially observed point process models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(3), pages 413-437, June.
    14. Varughese, Melvin M., 2013. "Parameter estimation for multivariate diffusion systems," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 417-428.
    15. Mark Bognanni & John Zito, 2019. "Sequential Bayesian Inference for Vector Autoregressions with Stochastic Volatility," Working Papers 19-29, Federal Reserve Bank of Cleveland.
    16. Marcin Kacperczyk & Paul Damien & Stephen G. Walker, 2013. "A new class of Bayesian semi-parametric models with applications to option pricing," Quantitative Finance, Taylor & Francis Journals, vol. 13(6), pages 967-980, May.
    17. Bounnite Mohamed Yasser & Nasroallah Abdelaziz, 2015. "Widening and clustering techniques allowing the use of monotone CFTP algorithm," Monte Carlo Methods and Applications, De Gruyter, vol. 21(4), pages 301-312, December.
    18. Osnat Stramer & Jun Yan, 2007. "Asymptotics of an Efficient Monte Carlo Estimation for the Transition Density of Diffusion Processes," Methodology and Computing in Applied Probability, Springer, vol. 9(4), pages 483-496, December.
    19. Saifuddin Syed & Alexandre Bouchard‐Côté & George Deligiannidis & Arnaud Doucet, 2022. "Non‐reversible parallel tempering: A scalable highly parallel MCMC scheme," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(2), pages 321-350, April.
    20. Brignone, Riccardo & Gonzato, Luca & Lütkebohmert, Eva, 2023. "Efficient Quasi-Bayesian Estimation of Affine Option Pricing Models Using Risk-Neutral Cumulants," Journal of Banking & Finance, Elsevier, vol. 148(C).

    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:istatr:v:89:y:2021:i:2:p:237-249. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/isiiinl.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.