The Hamming Ball Sampler

TL;DR

The paper presents the Hamming Ball Sampler, an innovative MCMC algorithm that efficiently explores high-dimensional discrete spaces by adaptively truncating the model space, balancing statistical efficiency and computational feasibility.

Contribution

It introduces a new MCMC method that generalizes Gibbs sampling for discrete models, enabling polynomial-time exploration of complex high-dimensional spaces.

Findings

Effective in high-dimensional discrete models

Balances efficiency and computational cost

Applicable to various statistical models

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 in polynomial time. The approach generalizes conventional Gibbs sampling schemes for discrete spaces and can be considered as a Big Data-enabled MCMC algorithm that 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.