Marginal AMP Chain Graphs
Abstract
We present a new family of models that is based on graphs that may have undirected, directed and bidirected edges. We name these new models marginal AMP (MAMP) chain graphs because each of them is Markov equivalent to some AMP chain graph under marginalization of some of its nodes. However, MAMP chain graphs do not only subsume AMP chain graphs but also multivariate regression chain graphs. We describe global and pairwise Markov properties for MAMP chain graphs and prove their equivalence for compositional graphoids. We also characterize when two MAMP chain graphs are Markov equivalent. For Gaussian probability distributions, we also show that every MAMP chain graph is Markov equivalent to some directed and acyclic graph with deterministic nodes under marginalization and conditioning on some of its nodes. This is important because it implies that the independence model represented by a MAMP chain graph can be accounted for by some data generating process that is partially observed and has selection bias. Finally, we modify MAMP chain graphs so that they are closed under marginalization for Gaussian probability distributions. This is a desirable feature because it guarantees parsimonious models under marginalization.
Cite
@article{arxiv.1305.0751,
title = {Marginal AMP Chain Graphs},
author = {Jose M. Peña},
journal= {arXiv preprint arXiv:1305.0751},
year = {2014}
}
Comments
Changes from v1 to v2: Discussion section got extended. Changes from v2 to v3: New Sections 3 and 5. Changes from v3 to v4: Example 4 added to discussion section. Changes from v4 to v5: None. Changes from v5 to v6: Some minor and major errors have been corrected. The latter include the definitions of descending route and pairwise separation base, and the proofs of Theorems 5 and 6