  We consider the problem of characterizing Bayesian networks up to
unconditional equivalence, i.e., when directed acyclic graphs (DAGs) have the
same set of unconditional $d$-separation statements. Each unconditional
equivalence class (UEC) is uniquely represented with an undirected graph whose
clique structure encodes the members of the class. Via this structure, we
provide a transformational characterization of unconditional equivalence; i.e.,
we show that two DAGs are in the same UEC if and only if one can be transformed
into the other via a finite sequence of specified moves. We also extend this
characterization to the essential graphs representing the Markov equivalence
classes (MECs) in the UEC. UECs partition the space of MECs and are easily
estimable from marginal independence tests. Thus, a characterization of
unconditional equivalence has applications in methods that involve searching
the space of MECs of Bayesian networks.
