Résumé en anglais

We discuss a parametric family of binary distributions for modeling and generating multivariate binary data with strong dependencies in dimensions too large for exhaustive enumeration of the state space. The proposed parametric family is shown to encompass any feasible combination of mean vector and correlation matrix. The approach goes beyond the range of dependencies achievable with methods discussed heretofore in the literature which we systematically review in this paper. We can both sample from the parametric family and evaluate its mass function point-wise which allows for immediate use in the context of stochastic optimization, importance sampling or Markov chain algorithms.