A comparison of a Gaussian and a binary ancestral graph model

For an ancestral graph with four vertices, we show that the associated binary model exhibits different properties than the previously studied Gaussian analog. The Gaussian likelihood function may be multimodal, whereas the likelihood function of the binary model is guaranteed to be unimodal. Canonical hidden variable models associated with ancestral graph models impose additional polynomial constraints of non-independence type in the binary case, but no additional constraints in the Gaussian case. Running title: Gaussian and binary ancestral graph models