Bayesian Networks

Question

I am working on following bayesian graph Graph

Here I am trying to calculate probability of the following P(W,f)=? I started as follow P(w,f)=P(W/f).p(F)

P(W/f)=P(W/R,S,f).P(R.S/F)+P(W/-R,s,f).P(-R.S/F)+P(W/R,-S,F).P(R.-S/F)+P(W/-R,-S,F).P(-R.-S/F) Since W is independent of F given R,S so P(W/f)=P(W/R,S).P(R.S/F)+P(W/-R,s).P(-R.S/F)+P(W/R,-S).P(R.-S/F)+P(W/-R,-S).P(-R.-S/F)

Here next I don't know what is the probability of P(R,s/F)??? Please any suggestion

Answer 1

Don't start like that. The method is:

1. Add in all other variables to get the full joint, e.g., just with S: P(W,F)=\sum_x P(W,F,S=x)
2. Simplify your full joint with conditional independences: P(W,F)=\sum_x P(F)P(W|S=x)P(S=x)

Add in all your variables, not just S.