 
Summary: G53KRR handout on Bayesian networks.
Bayesian approach (subjective probability) The basic idea is that we assign degrees of
belief (subjective probabilities) to statements like "Tweety can fly" or "Patient a has disease
b". Both sentences are either true or false in the real world, so standard objective statistical
probabilities don't apply. However we can base our degree of belief on statistical information:
namely, if 95% of birds can fly we may believe with degree 95% that a particular bird Tweety can
fly. This will be an a priori degree of belief, before we know anything else about Tweety. Once
we discover other facts about Tweety, our belief will be based on the conditional probability that
Tweety flies given other facts (that it is a penguin for example).
Suppose there are n propositional variables of interest: p1, . . . , pn. There are 2n
possible states
of the world I  truth assignments to those variables. J is a joint probability distribution if for
every assignment I, J(I) is a number between 0 and 1 and J(I) = 1. The probability of a
sentence is the sum of probabilities of the worlds where is true:
Pr() = I=J(I)
Conditional probability of given is defined as follows:
Pr(  ) =
Pr( )
Pr()
Unfortunaly, this requires us to keep 2n
