• Lecture notes on Bayes Rule & Bayesian Networks
• Josh Tenenbaum MIT professor doing research in cognitive science

Marginal: Probability of one event at a time regardless of what happens to other events.

Conditional: Probability of one event given another event (rows sum to 1).

Joint: Probability of both events occurring (all the values sum to 1).

Expected Utility (EU) =

Sum Over All Possible Events {Utility of the Event * Probability of the Event}

EU is called "Best Response" in Game Theory and if the participants use it, they reach "Nash Equilibrium"

• Nodes are random variables
• Edges are direct influence 
• Acyclic means no cycles (closed group)
• Directed means arrows showing what influences what
• Statastical dependence does not imply causation (correlation is not causation)
• To prove causation, need to explore further
• DAG tells that the joint probability of all the variables is a product of conditional probabilities of individual variables given their parents

P(B,E,A,R,C)

= P(B) P(E|B) P(A|B,E) P(R|A,B,E) P(C|R,A,B,E)

= P(B) P(E) P(A|B,E) P(R|E) P(C|A)