Suppose, instead that we were to observe a value for A and a value for I. What are the factors created by the observations? Given the variable ordering, K, B, D, C, E, G, F, H. For each step show which factors are removed and what factor is created.
Observing A results in replacing the factor P(A) with f_{1}() (i.e., just a number that isn't a function of any variable. It isn't needed to compute the posterior probability of any variable; it may be useful is we want the prior probability of the observations), replacing the factor P(C|A) with f_{2}(C), and replacing the factor P(D|A,B) with f_{3}(D,B).
Observing I results in replacing the factor P(I|F,G) with f_{4}(F,G), the factor P(J|H,I) with f_{5}(J,H) and P(K|I) with f_{6}(K).
Note that f_{7} is the constant 1 (as it is P(k|i)+P(¬k|i)).
Step Eliminate Removed Added 1. K f_{6}(K) f_{7} 2. B P(B), f_{3}(D,B) f_{8}(D) 3. D P(F|D), f_{8}(D) f_{9}(F) 4. C P(E|C), f_{2}(C) f_{10}(E) 5. E P(H|E,F),f_{10}(E) f_{11}(H,F) 6. G P(G), f_{4}(F,G) f_{12}(F) 7. F f_{9}(F), f_{11}(H,F), f_{12}(F) f_{13}(H) 8. H f_{5}(H,J), f_{13}(H) f_{14}(J)