On parametric families for sampling binary data with specified mean and   correlation
  We discuss a class of binary parametric families with conditional probabilities taking the form of generalized linear models and show that this approach allows to model high-dimensional random binary vectors with arbitrary mean and correlation. We derive the special case of logistic conditionals as an approximation to the Ising-type exponential distribution and provide empirical evidence that this parametric family indeed outperforms competing approaches in terms of feasible correlations. 
Christian Sch\"afer
stat.ME stat.CO