D-separation

is_d_separated(dag, x, y, cond; ignore_edges)

Checks that X variables are independent on Y variables being conditioned on third set of variables. Three sets could be given as vectors of node labels (Symbol) or as vectors of node indices in the underlying graph. Used NetworkX d_separated implementation.

Argument ignore_edges can contain list of node pairs of edges to be ignored during the test.

Examples

julia> using Dagitty

julia> g = DAG(:A => :C, :C => :B)
DAG: {3, 2} directed simple Int64 graph with labels [:A, :B, :C])

julia> is_d_separated(g, [:A], [:B], [:C])
true

julia> is_d_separated(g, [:A], [:C], [:B])
false

julia> is_d_separated(g, [1], [2], [3])
true

julia> g = DAG(:A => :B, :A => :C, :C => :B)
DAG: {3, 3} directed simple Int64 graph with labels [:A, :B, :C])

julia> is_d_separated(g, [:A], [:B], [:C], ignore_edges=[:A => :B])
true

ConditionalIndependence

Structure representing conditional independency between two variables given conditioned set of variables.

implied_conditional_independencies(dag)

From given DAG find all pair-wise conditional independencies of nodes. Returns vector of ConditionalIndependence structures.

Examples

julia> using Dagitty

julia> g = DAG(:A => :C, :C => :B)
DAG: {3, 2} directed simple Int64 graph with labels [:A, :B, :C])

julia> implied_conditional_independencies(g)
1-element Vector{ConditionalIndependence}:
 ConditionalIndependence(:A, :B, [:C])

implied_conditional_independencies_min

From given DAG return all pair-wise conditional independencies of nodes with minimal condition set.

Examples

julia> using Dagitty

julia> plant_dag = Dagitty.DAG(:H_0 => :H_1, :F => :H_1, :T => :F)
DAG: {4, 3} directed simple Int64 graph with labels [:F, :H_0, :H_1, :T])

julia> implied_conditional_independencies_min(plant_dag)
3-element Vector{ConditionalIndependence}:
 ConditionalIndependence(:F, :H_0, Symbol[])
 ConditionalIndependence(:H_0, :T, Symbol[])
 ConditionalIndependence(:H_1, :T, [:F])