A subcopula characterization of dependence for the Multivariate Bernoulli Distribution

Abstract

By applying Sklar's theorem to the Multivariate Bernoulli Distribution (MBD), this paper proposes a framework to decouple marginal distributions from the dependence structure, clarifying interactions among binary variables. Explicit formulas are derived under the MBD 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 of the MBD, offering practical tools for parameter estimation and dependence analysis in real-world applications. The results obtained contribute to the application of subcopulas of multivariate binary data, with real data examples.