A subcopula characterization of dependence for the Multivariate Bernoulli Distribution

TL;DR

This paper introduces a novel framework using subcopulas to characterize and measure complex dependence structures in multivariate Bernoulli distributions, enhancing understanding and estimation of binary variable interactions.

Contribution

It applies Sklar's theorem to MBDs, deriving explicit formulas for dependence measures of all orders and proposing a Bayesian inference method for parameter estimation.

Findings

Explicit formulas for dependence measures of all orders.

Bayesian inference approach for parameter estimation.

Application to real-world binary data examples.

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.