Graphical Markov Models with Mixed Graphs in R

In this paper we provide a short tutorial illustrating the new functions in the package ggm that deal with ancestral, summary and ribbonless graphs. These are mixed graphs (containing three types of edges) that are important because they capture the modified inde- pendence structure after marginalisation over, and conditioning on, nodes of directed acyclic graphs. We provide functions to verify whether a mixed graph implies that A is independent of B given C for any disjoint sets of nodes and to generate maximal graphs inducing the same independence structure of nonmaximal graphs. Finally, we provide functions to decide on the Markov equivalence of two graphs with the same node set but different types of edges.