Admissible Bernoulli Correlations

Nevena Maric; Mark Huber

doi:10.1186/s40488-019-0091-5

Admissible Bernoulli Correlations

Nevena Maric, Mark Huber

University of Missouri-St. Louis

Research output: Contribution to journal › Article › peer-review

Abstract

A multivariate symmetric Bernoulli distribution has marginals that are uniform over the pair {0, 1}. Consider the problem of sampling from this distribution given a prescribed correlation between each pair of variables. Not all correlation structures can be attained. Here we completely characterize the admissible correlation vectors as those given by convex combinations of simpler distributions. This allows us to bijectively relate the correlations to the well-known CUTn polytope, as well as determine if the correlation is possible through a linear programming formulation.

Original language	American English
Journal	Journal of Statistical Distributions and Applications
Volume	6
DOIs	https://doi.org/10.1186/s40488-019-0091-5
State	Published - Mar 8 2019

Disciplines

Mathematics

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Cite this

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title = "Admissible Bernoulli Correlations",

abstract = " A multivariate symmetric Bernoulli distribution has marginals that are uniform over the pair {0, 1}. Consider the problem of sampling from this distribution given a prescribed correlation between each pair of variables. Not all correlation structures can be attained. Here we completely characterize the admissible correlation vectors as those given by convex combinations of simpler distributions. This allows us to bijectively relate the correlations to the well-known CUTn polytope, as well as determine if the correlation is possible through a linear programming formulation.",

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AB - A multivariate symmetric Bernoulli distribution has marginals that are uniform over the pair {0, 1}. Consider the problem of sampling from this distribution given a prescribed correlation between each pair of variables. Not all correlation structures can be attained. Here we completely characterize the admissible correlation vectors as those given by convex combinations of simpler distributions. This allows us to bijectively relate the correlations to the well-known CUTn polytope, as well as determine if the correlation is possible through a linear programming formulation.

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DO - 10.1186/s40488-019-0091-5

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JO - Journal of Statistical Distributions and Applications

JF - Journal of Statistical Distributions and Applications

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