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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.

Original publication

DOI

10.1080/01621459.2016.1222288

Type

Journal article

Journal

J Am Stat Assoc

Publication Date

2017

Volume

112

Pages

1598 - 1611

Keywords

Bayesian, Discrete state spaces, Markov chain Monte Carlo