pairMarkov -- Pairwise Markov statements for a directed graph.

Synopsis

Usage:
pairMarkov G
Inputs:
- G, an object of class Digraph
Outputs:
- L, a list, whose entries are triples A,B,C representing pairwise Markov conditional independence statements of the form ”A is independent of B given C” that hold for G.

Description

Given a directed graph G, pairwise Markov statements are statements of the form {v,w,nondescendents(G,v)-w}for each vertex v of G. In other words, for every vertex v of G and all nondescendents w of v, v is independent of w given all other nondescendents.

For example, for the digraph D on 4 vertices with edges a->b, a->c, b->c, and b->d, we get the following pairwise Markov statements:

i1 : D = digraph {{a,{b,c}}, {b,{c,d}}, {c,{}}, {d,{}}}

o1 = Digraph{a => set {b, c}}
             b => set {c, d}
             c => set {}
             d => set {}

o1 : Digraph

i2 : L = pairMarkov D

o2 = {{{c}, {d}, {b, a}}, {{a}, {d}, {b, c}}}

o2 : List

Note that the method displays only non-redundant statements.

Ways to use `pairMarkov` :

pairMarkov(Digraph)

pairMarkov -- Pairwise Markov statements for a directed graph.

Synopsis

Description

See also

Ways to use pairMarkov :

Ways to use `pairMarkov` :