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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




Journal article


Journal of the American Statistical Association

Publication Date





1598 - 1611


Department of Informatics, Athens University of Economics and Business, Athens, Greece.