Querying Information
\(Pr(x_1,...x_n)=\prod\limits_{i=1}^{n} Pr(x_i|\,parents(X_i))\)
For probabilities not specified, we need to take the sum of all possibilities inside the products.
Conditional Independence
A node is conditionally independent of its other predecessors, given its parents.
Each variable is conditionally independent of its non-descendents, given its parents
Markov blanket: A node is conditionally independent of all other nodes in the blanket, given its parents, children, and children’s parents.
Three Conditions for all paths
Common parent known
Middle of chain known
Common child unknown
Bayes rule: flip