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2020 On finite exchangeability and conditional independence
Kayvan Sadeghi
Electron. J. Statist. 14(2): 2773-2797 (2020). DOI: 10.1214/20-EJS1730

Abstract

We study the independence structure of finitely exchangeable distributions over random vectors and random networks. In particular, we provide necessary and sufficient conditions for an exchangeable vector so that its elements are completely independent or completely dependent. We also provide a sufficient condition for an exchangeable vector so that its elements are marginally independent. We then generalize these results and conditions for exchangeable random networks. In this case, it is demonstrated that the situation is more complex. We show that the independence structure of exchangeable random networks lies in one of six regimes that are two-fold dual to one another, represented by undirected and bidirected independence graphs in graphical model sense with graphs that are complement of each other. In addition, under certain additional assumptions, we provide necessary and sufficient conditions for the exchangeable network distributions to be faithful to each of these graphs.

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Kayvan Sadeghi. "On finite exchangeability and conditional independence." Electron. J. Statist. 14 (2) 2773 - 2797, 2020. https://doi.org/10.1214/20-EJS1730

Information

Received: 1 April 2020; Published: 2020
First available in Project Euclid: 22 July 2020

zbMATH: 1446.62255
MathSciNet: MR4125857
Digital Object Identifier: 10.1214/20-EJS1730

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Vol.14 • No. 2 • 2020
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