A Subcopula Characterization of Dependence for the Multivariate Bernoulli Distribution

This paper provides a subcopula characterization of dependence for the Multivariate Bernoulli Distribution. Explicit formulas are derived using subcopulas to introduce dependence measures for interactions of all orders, not just pairwise. A Bayesian inference approach is also applied to estimate the parameters, offering practical tools for parameter estimation and dependence analysis in real-world applications. The main contribution is an explicit, order-by-order characterization of multivariate dependence for binary data (beyond pairwise association), linking joint probabilities to subcopula-based dependence parameters/measures under full compatibility; this fills a gap in the literature where practical modeling often stops at pairwise dependence.