  Motivated by the problem of designing inference-friendly Bayesian
nonparametric models in probabilistic programming languages, we introduce a
general class of partially exchangeable random arrays which generalizes the
notion of hierarchical exchangeability introduced in Austin and Panchenko
(2014). We say that our partially exchangeable arrays are DAG-exchangeable
since their partially exchangeable structure is governed by a collection of
Directed Acyclic Graphs. More specifically, such a random array is indexed by
$\mathbb{N}^{|V|}$ for some DAG $G=(V,E)$, and its exchangeability structure is
governed by the edge set $E$. We prove a representation theorem for such arrays
which generalizes the Aldous-Hoover and Austin-Panchenko representation
theorems.
