localMarkov -- Local Markov statements for a directed graph.

Synopsis

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

Description

Given a directed graph G, local Markov statements are of the form {v, nondescendents(v) - parents(v), parents(v)}. That is, every vertex v of G is independent of its nondescendents (excluding parents) given the parents.

For example, for the digraph D on 4 vertices with edges a->b, a->c, b->c, and b->d, we get the following local 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 = localMarkov D

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

o2 : List

Note that the method displays only non-redundant statements.

Ways to use `localMarkov` :

localMarkov(Digraph)

localMarkov -- Local Markov statements for a directed graph.

Synopsis

Description

See also

Ways to use localMarkov :

Ways to use `localMarkov` :