  This paper deals with chain graphs under the Andersson-Madigan-Perlman (AMP)
interpretation. In particular, we present a constraint based algorithm for
learning an AMP chain graph a given probability distribution is faithful to.
Moreover, we show that the extension of Meek's conjecture to AMP chain graphs
does not hold, which compromises the development of efficient and correct
score+search learning algorithms under assumptions weaker than faithfulness.
  We also introduce a new family of graphical models that consists of
undirected and bidirected edges. We name this new family maximal
covariance-concentration graphs (MCCGs) because it includes both covariance and
concentration graphs as subfamilies. However, every MCCG can be seen as the
result of marginalizing out some nodes in an AMP CG. We describe global, local
and pairwise Markov properties for MCCGs and prove their equivalence. We
characterize when two MCCGs are Markov equivalent, and show that every Markov
equivalence class of MCCGs has a distinguished member. We present a constraint
based algorithm for learning a MCCG a given probability distribution is
faithful to.
  Finally, we present a graphical criterion for reading dependencies from a
MCCG of a probability distribution that satisfies the graphoid properties, weak
transitivity and composition. We prove that the criterion is sound and complete
in certain sense.
