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A Bootstrap Metropolis-Hastings Algorithm for Bayesian Analysis of Big Data.

Faming Liang1, Jinsu Kim2, Qifan Song3

  • 1Professor, Department of Biostatistics, University of Florida, Gainesville, FL 32611.

Technometrics : a Journal of Statistics for the Physical, Chemical, and Engineering Sciences
|October 17, 2017
PubMed
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We introduce the bootstrap Metropolis-Hastings (BMH) algorithm, a novel method enabling powerful Markov chain Monte Carlo (MCMC) techniques for big data analysis by utilizing parallel bootstrap samples. This approach makes complex data analysis feasible for large datasets.

Area of Science:

  • Computational Statistics
  • Data Science
  • Machine Learning

Background:

  • Markov chain Monte Carlo (MCMC) methods are powerful for complex data but computationally intensive.
  • Traditional MCMC methods are unsuitable for big data due to high computational demands and full dataset scans per iteration.

Purpose of the Study:

  • To propose a novel algorithm, bootstrap Metropolis-Hastings (BMH), for adapting MCMC methods to big data analysis.
  • To provide a general framework for making computationally intensive MCMC methods feasible for large-scale datasets.

Main Methods:

  • The bootstrap Metropolis-Hastings (BMH) algorithm replaces the full data log-likelihood with a Monte Carlo average from parallel bootstrap samples.
  • The BMH algorithm exhibits an embarrassingly parallel structure, avoiding repeated full dataset scans.
Keywords:
Big DataBootstrapMarkov Chain Monte CarloMetropolis-HastingsParallel Computing

Related Experiment Videos

  • BMH can be extended, demonstrated by the tempering BMH algorithm combining parallel tempering with BMH.
  • Main Results:

    • The BMH algorithm is shown to be feasible for big data problems.
    • BMH can be more efficient than divide-and-combine methods, integrating full data information in a single run.
    • The flexibility of BMH is demonstrated through its use in advanced MCMC algorithms, model selection, and optimization.

    Conclusions:

    • The bootstrap Metropolis-Hastings (BMH) algorithm offers a general and flexible framework for big data analysis using MCMC methods.
    • BMH enhances computational efficiency and scalability, making complex statistical analysis accessible for large datasets.
    • BMH serves as a foundational block for developing advanced, big data-compatible MCMC techniques.