Exchangeable Bernoulli distributions: high dimensional simulation, estimate and testing

TL;DR

This paper investigates the geometrical structure of exchangeable Bernoulli distributions, providing analytical tools for high-dimensional simulation, estimation, and hypothesis testing of binary data with complex correlation structures.

Contribution

It introduces a geometric framework for exchangeable Bernoulli distributions, enabling precise simulation, bounds, and testing methods for high-dimensional correlated binary data.

Findings

Analytical expressions for extremal generators of the distribution class

Methods for high-dimensional simulation of negatively correlated binary data

Sharp bounds and distributional results for statistical indices

Abstract

We explore the class of exchangeable Bernoulli distributions building on their geometrical structure. Exchangeable Bernoulli probability mass functions are points in a convex polytope and we have found analytical expressions for their extremal generators. The geometrical structure turns out to be crucial to simulate high dimensional and negatively correlated binary data. Furthermore, for a wide class of statistical indices and measures of a probability mass function we are able to find not only their sharp bounds in the class, but also their distribution across the class. Estimate and testing are also addressed.