A de Finetti-type representation of joint hierarchically exchangeable arrays on directed acyclic graphs

Jiho Lee

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arXiv · 2006.13091

A de Finetti-type representation of joint hierarchically exchangeable arrays on directed acyclic graphs

Jiho Lee

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Abstract

We define joint exchangeability on arrays indexed by a vector of natural numbers with coordinates being the vertices of directed acyclic graphs (DAGs) using local isomorphisms. The notion provides a new version of exchangeability, which is a joint version of hierarchical exchangeability defined in Jung, L., Staton, Yang (2020). We also prove the existence of a generic representation by independent uniform random variables.

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Jiho Lee. 2020-06-23. A de Finetti-type representation of joint hierarchically exchangeable arrays on directed acyclic graphs. https://arxiv.org/abs/2006.13091

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