Full joint distribution specifies answer to any query:
P(variable | evidence about others)
Reasoning using BNs
Probability theory is nothing but
common sense reduced to calculation.
Pierre Simon Laplace
The product of the CPTs represents the full joint distribution over the variables.
This distrib specifies answers to
Queries of the form P(X|E).
The encoded distribution supports very subtle reasoning patterns:
Suppose we find out that the letter was positive – the probability of high grade will go up, increasing
The prob of high intell and decreasing the prob of difficulty of a class.
However if we later find out that the student has high SAT score,
The prob of intell goes up higher, and now the prob of the class difficulty increases.