Local Markov Property for Models Satisfying Composition Axiom
  The local Markov condition for a DAG to be an independence map of a
probability distribution is well known. For DAGs with latent variables,
represented as bi-directed edges in the graph, the local Markov property may
invoke exponential number of conditional independencies. This paper shows that
the number of conditional independence relations required may be reduced if the
probability distributions satisfy the composition axiom. In certain types of
graphs, only linear number of conditional independencies are required. The
result has applications in testing linear structural equation models with
correlated errors.
