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The Hamming Ball Sampler

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  • Michalis K. Titsias
  • Christopher Yau

Abstract

We introduce the Hamming ball sampler, a novel Markov chain Monte Carlo algorithm, for efficient inference in statistical models involving high-dimensional discrete state spaces. The sampling scheme uses an auxiliary variable construction that adaptively truncates the model space allowing iterative exploration of the full model space. The approach generalizes conventional Gibbs sampling schemes for discrete spaces and provides an intuitive means for user-controlled balance between statistical efficiency and computational tractability. We illustrate the generic utility of our sampling algorithm through application to a range of statistical models. Supplementary materials for this article are available online.

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  • Michalis K. Titsias & Christopher Yau, 2017. "The Hamming Ball Sampler," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1598-1611, October.
    • Handle: RePEc:taf:jnlasa:v:112:y:2017:i:520:p:1598-1611
    DOI: 10.1080/01621459.2016.1222288
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    References listed on IDEAS

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    1. Yanxun Xu & Peter Müller & Yuan Yuan & Kamalakar Gulukota & Yuan Ji, 2015. "MAD Bayes for Tumor Heterogeneity--Feature Allocation With Exponential Family Sampling," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 503-514, June.
    2. Hans, Chris & Dobra, Adrian & West, Mike, 2007. "Shotgun Stochastic Search for," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 507-516, June.
    3. Tomi Peltola & Pekka Marttinen & Aki Vehtari, 2012. "Finite Adaptation and Multistep Moves in the Metropolis-Hastings Algorithm for Variable Selection in Genome-Wide Association Analysis," PLOS ONE, Public Library of Science, vol. 7(11), pages 1-11, November.
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    Cited by:

    1. Quan Zhou & Jun Yang & Dootika Vats & Gareth O. Roberts & Jeffrey S. Rosenthal, 2022. "Dimension‐free mixing for high‐dimensional Bayesian variable selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(5), pages 1751-1784, November.

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