Reasoning with alternative acyclic directed mixed graphs

Causal Effect Identification in Alternative Acyclic Directed Mixed Graphs

Alternative acyclic directed mixed graphs (ADMGs) are graphs that may allow causal effect identification in scenarios where Pearl’s original ADMGs may not, and vice versa. Therefore, they complement each other. In this paper, we introduce a sound algorithm for identifying arbitrary causal effects from alternative ADMGs. Moreover, we show that the algorithm is complete for identifying the causal...

Alternative Markov and Causal Properties for Acyclic Directed Mixed Graphs

We extend Andersson-Madigan-Perlman chain graphs by (i) relaxing the semidirected acyclity constraint so that only directed cycles are forbidden, and (ii) allowing up to two edges between any pair of nodes. We introduce global, and ordered local and pairwise Markov properties for the new models. We show the equivalence of these properties for strictly positive probability distributions. We also...

Alternative Markov Properties for Acyclic Directed Mixed Graphs

We extend AMP chain graphs by (i) relaxing the semidirected acyclity constraint so that only directed cycles are forbidden, and (ii) allowing up to two edges between any pair of nodes. We introduce global, ordered local and pairwise Markov properties for the new models. We show the equivalence of these properties for strictly positive probability distributions. We also show that when the random...

Markov Properties for Acyclic Directed Mixed Graphs

We consider acyclic directed mixed graphs, in which directed edges (x → y) and bi-directed edges (x ↔ y) may occur. A simple extension of Pearl’s d-separation criterion, called m-separation, is applied to these graphs. We introduce a local Markov property which is equivalent to the global property resulting from the m-separation criterion.

Generic Directed Acyclic Graphs