2. Structure and Semantics of BN
draw causal nodes first
draw directed edges to effects (“direct causes”)
links encode conditional probability tables
absence of link implies conditional independence given parents
advantage: fewer parameters than full joint prob table (25=32 entries in this case)

3. Equation for full joint probability=

4. Inference in Bayesian Nets
Objective: calculate posterior probability of a variable X conditioned on evidence Y and marginalizing over Z (unobserved variables)
suppose we wanted to know the probability that there was a burglary (B) given that john calls (j) and mary calls (m) (but we don’t know alarm or earthquake)
so the conditional prob is proportional to joint prob.
next, we marginalize over unobserved vars e and a...
full joint
rearrange

6. Lumiere – Office Assistant