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Subsampling MCMC - an Introduction for the Survey Statistician

Author

Listed:
  • Matias Quiroz

    (University of New South Wales)

  • Mattias Villani

    (Stockholm University
    Linköping University)

  • Robert Kohn

    (University of New South Wales)

  • Minh-Ngoc Tran

    (University of Sydney)

  • Khue-Dung Dang

    (University of New South Wales)

Abstract

The rapid development of computing power and efficient Markov Chain Monte Carlo (MCMC) simulation algorithms have revolutionized Bayesian statistics, making it a highly practical inference method in applied work. However, MCMC algorithms tend to be computationally demanding, and are particularly slow for large datasets. Data subsampling has recently been suggested as a way to make MCMC methods scalable on massively large data, utilizing efficient sampling schemes and estimators from the survey sampling literature. These developments tend to be unknown by many survey statisticians who traditionally work with non-Bayesian methods, and rarely use MCMC. Our article explains the idea of data subsampling in MCMC by reviewing one strand of work, Subsampling MCMC, a so called Pseudo-Marginal MCMC approach to speeding up MCMC through data subsampling. The review is written for a survey statistician without previous knowledge of MCMC methods since our aim is to motivate survey sampling experts to contribute to the growing Subsampling MCMC literature.

Suggested Citation

  • Matias Quiroz & Mattias Villani & Robert Kohn & Minh-Ngoc Tran & Khue-Dung Dang, 2018. "Subsampling MCMC - an Introduction for the Survey Statistician," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 33-69, December.
  • Handle: RePEc:spr:sankha:v:80:y:2018:i:1:d:10.1007_s13171-018-0153-7
    DOI: 10.1007/s13171-018-0153-7
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    References listed on IDEAS

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    1. David M. Blei & Alp Kucukelbir & Jon D. McAuliffe, 2017. "Variational Inference: A Review for Statisticians," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 859-877, April.
    2. Alexandre Bouchard-Côté & Sebastian J. Vollmer & Arnaud Doucet, 2018. "The Bouncy Particle Sampler: A Nonreversible Rejection-Free Markov Chain Monte Carlo Method," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 855-867, April.
    3. Håvard Rue & Sara Martino & Nicolas Chopin, 2009. "Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 319-392, April.
    4. Flury, Thomas & Shephard, Neil, 2011. "Bayesian Inference Based Only On Simulated Likelihood: Particle Filter Analysis Of Dynamic Economic Models," Econometric Theory, Cambridge University Press, vol. 27(5), pages 933-956, October.
    5. Pitt, Michael K. & Silva, Ralph dos Santos & Giordani, Paolo & Kohn, Robert, 2012. "On some properties of Markov chain Monte Carlo simulation methods based on the particle filter," Journal of Econometrics, Elsevier, vol. 171(2), pages 134-151.
    6. Chang-Han Rhee & Peter W. Glynn, 2015. "Unbiased Estimation with Square Root Convergence for SDE Models," Operations Research, INFORMS, vol. 63(5), pages 1026-1043, October.
    7. George Deligiannidis & Arnaud Doucet & Michael K. Pitt, 2018. "The correlated pseudomarginal method," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(5), pages 839-870, November.
    8. A. Doucet & M. K. Pitt & G. Deligiannidis & R. Kohn, 2015. "Efficient implementation of Markov chain Monte Carlo when using an unbiased likelihood estimator," Biometrika, Biometrika Trust, vol. 102(2), pages 295-313.
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    Cited by:

    1. Dang, Khue-Dung & Quiroz, Matias & Kohn, Robert & Tran, Minh-Ngoc & Villani, Mattias, 2019. "Hamiltonian Monte Carlo with Energy Conserving Subsampling," Working Paper Series 372, Sveriges Riksbank (Central Bank of Sweden).

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