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Fast, approximate MCMC for Bayesian analysis of large data sets: A design based approach

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  • Kaeding, Matthias

Abstract

We propose a fast approximate Metropolis-Hastings algorithm for large data sets embedded in a design based approach. Here, the loglikelihood ratios involved in the Metropolis-Hastings acceptance step are considered as data. The building block is one single subsample from the complete data set, so that the necessity to store the complete data set is bypassed. The subsample is taken via the cube method, a balanced sampling design, which is defined by the property that the sample mean of some auxiliary variables is close to the sample mean of the complete data set. We develop several computationally and statistically efficient estimators for the Metropolis-Hastings acceptance probability. Our simulation studies show that the approach works well and can lead to results which are close to the use of the complete data set, while being much faster. The methods are applied on a large data set consisting of all German diesel prices for the first quarter of 2015.

Suggested Citation

  • Kaeding, Matthias, 2016. "Fast, approximate MCMC for Bayesian analysis of large data sets: A design based approach," Ruhr Economic Papers 660, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    • Handle: RePEc:zbw:rwirep:660
    DOI: 10.4419/86788766
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    References listed on IDEAS

    as
    1. Guillaume Chauvet & Yves Tillé, 2006. "A fast algorithm for balanced sampling," Computational Statistics, Springer, vol. 21(1), pages 53-62, March.
    2. Jean-Claude Deville & Yves Tille, 2004. "Efficient balanced sampling: The cube method," Biometrika, Biometrika Trust, vol. 91(4), pages 893-912, December.
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    More about this item

    Keywords

    Bayesian inference; big data; approximate MCMC; survey sampling;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis
    • C83 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Survey Methods; Sampling Methods

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