Marginal AMP Chain Graphs release_kgewc5zblbav3c3wv3z2yp2vfm

by Jose M. Peña

Released as a article .

2014  

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.
In text/plain format

Archived Files and Locations

application/pdf  420.3 kB
file_35emmj2l45cfngq6jbmvr2n2pq
web.archive.org (webarchive)
arxiv.org (repository)
Read Archived PDF
Archived
Type  article
Stage   submitted
Date   2014-11-07
Version   v6
Language   en ?
arXiv  1305.0751v6
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)
Catalog Record
Revision: 4ff133ad-241a-47ea-a431-c449cc255ebf
API URL: JSON