Marginal AMP Chain Graphs

We present a new family of graphical models that may have undirected, directed and bidirected edges. We name these new models marginal AMP (MAMP) chain graphs because each of them can be seen as the result of marginalizing out some nodes in an AMP chain graph. However, MAMP chain graphs do not only subsume AMP chain graphs but also regression chain graphs. We describe global and local Markov properties for MAMP chain graphs and prove their equivalence for compositional graphoids. We also characterize when two MAMP chain graphs are Markov equivalent.