For the following Bayes nets, add the minimal number of arrows such that the resulting structure is able to represent all distributions that satisfy the stated independence and nonindependence constraints (note these are constraints on the Bayes net structure, so each nonindependence constraint should be interpreted as disallowing all structures that make the given independence assumption). If no arrows are needed, write “none needed.” If no such Bayes net is possible, write “not possible.”

a. See Figure S13.5 (a). Constraints: 

• A ⊥⊥ B 

• not A ⊥⊥ B | {C} 

b. See Figure S13.5 (b). Constraints: 

• A ⊥⊥ D | {C} 

• A ⊥⊥ B 

• B ⊥⊥ C 

• not A ⊥⊥ B | {D} 

c. See Figure S13.5 (b). Constraints: 

• A ⊥⊥ B 

• C ⊥⊥ D | {A, B} 

• not C ⊥⊥ D | {A} 

• not C ⊥⊥ D | {B}

 Figure S13.5 (a)

Figure S13.5 (b)

Transcribed Image Text:

A C (a) B