  We introduce finite mixtures of Ising models as a novel approach to study
multivariate patterns of associations of binary variables. Our proposed models
combine the strengths of Ising models and multivariate Bernoulli mixture
models. We examine conditions required for the identifiability of Ising mixture
models, and develop a Bayesian framework for fitting them. Through simulation
experiments and real data examples, we show that Ising mixture models lead to
meaningful results for sparse binary contingency tables.
