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Rao–Blackwellisation in the Markov Chain Monte Carlo Era

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  • 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
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    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. 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.
    4. Nicolas Chopin & Christian P. Robert, 2010. "Properties of nested sampling," Biometrika, Biometrika Trust, vol. 97(3), pages 741-755.
    5. repec:dau:papers:123456789/4645 is not listed on IDEAS
    6. 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.
    7. Tal Galili & Isaac Meilijson, 2016. "An Example of an Improvable Rao--Blackwell Improvement, Inefficient Maximum Likelihood Estimator, and Unbiased Generalized Bayes Estimator," The American Statistician, Taylor & Francis Journals, vol. 70(1), pages 108-113, February.
    8. 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.
    9. repec:dau:papers:123456789/4644 is not listed on IDEAS
    10. repec:dau:papers:123456789/10690 is not listed on IDEAS
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