Latent uniform samplers on multivariate binary spaces

We consider sampling from a probability distribution on {0,1}^M , or an equivalent high-dimensional binary space. A number of important applications rely on sampling from such distributions, including Bayesian variable selection problems and fitting Bayesian regression trees. Direct sampling is prohibitive when the dimension is large due to the fact that there are 2^M possible states. One approach to sampling such distributions is to use a Metropolis–Hastings algorithm, which can require choosing a decent proposal mechanism, with a default choice being the single-component switch proposal move. This is problematic when multiple modes exist. In this paper, we propose a latent variable uniform sampling algorithm, such as a latent slice sampler, which allows for large moves and proposal paths which give non-negligible probabilities for moving between modes, even when the probabilities of states between these modes is low. A number of illustrations are presented, focusing primarily on demonstrating the advantages over current generic samplers.