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Abstract: The main contributions of this work (joint with P. Semeraro, Politecnico di Torino) are the development of algorithms for sampling from multivariate Bernoulli distributions, as well as methods for determining the distributions and bounds of a broad class of indices and measures of probability mass functions.  Probability mass functions of exchangeable Bernoulli distributions can be represented as points in a convex polytope, for which we provide an analytical characterization of the extremal points. 

The more general class of multivariate Bernoulli distributions with identical marginal distributions, each with parameter p, also forms a convex polytope. However, identifying its extremal points is considerably more challenging. Our main theoretical contribution is the introduction of an algebraic approach that yields a set of analytically tractable generators.

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