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Simple, scalable and accurate posterior interval estimation

Author

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  • Cheng Li
  • Sanvesh Srivastava
  • David B. Dunson

Abstract

SummaryStandard posterior sampling algorithms, such as Markov chain Monte Carlo procedures, face major challenges in scaling up to massive datasets. We propose a simple and general posterior interval estimation algorithm to rapidly and accurately estimate quantiles of the posterior distributions for one-dimensional functionals. Our algorithm runs Markov chain Monte Carlo in parallel for subsets of the data, and then averages quantiles estimated from each subset. We provide strong theoretical guarantees and show that the credible intervals from our algorithm asymptotically approximate those from the full posterior in the leading parametric order. Our algorithm has a better balance of accuracy and efficiency than its competitors across a variety of simulations and a real-data example.

Suggested Citation

  • Cheng Li & Sanvesh Srivastava & David B. Dunson, 2017. "Simple, scalable and accurate posterior interval estimation," Biometrika, Biometrika Trust, vol. 104(3), pages 665-680.
  • Handle: RePEc:oup:biomet:v:104:y:2017:i:3:p:665-680.
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    File URL: http://hdl.handle.net/10.1093/biomet/asx033
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    Cited by:

    1. Niu, Baozhuang & Chen, Yuyang & Zeng, Fanzhuo, 2023. "One step further for procurement cooperation: Will the industry leader benefit from its competitive manufacturer's joint determination of consumption quality?," European Journal of Operational Research, Elsevier, vol. 311(3), pages 989-1008.
    2. Murray Pollock & Paul Fearnhead & Adam M. Johansen & Gareth O. Roberts, 2020. "Quasi‐stationary Monte Carlo and the ScaLE algorithm," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(5), pages 1167-1221, December.
    3. Lin Lin & Wei Shi & Jianbo Ye & Jia Li, 2023. "Multisource single‐cell data integration by MAW barycenter for Gaussian mixture models," Biometrics, The International Biometric Society, vol. 79(2), pages 866-877, June.

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