For each of the following programs:
Draw the dependency diagram (Bayes net). If you donâ€™t have software on your computer for doing this, Google Docs has a decent interface for creating drawings.
Use informal evaluation order reasoning and the intervention method to determine causal dependency between A and B.
Use conditioning to determine whether A and B are statistically dependent.
a)
var a = flip()
var b = flip()
var c = flip(a && b ? .8 : .5)
b)
var a = flip()
var b = flip(a ? .9 : .2)
var c = flip(b ? .7 : .1)
c)
var a = flip()
var b = flip(a ? .9 : .2)
var c = flip(a ? .7 : .1)
d)
var a = flip(.6)
var c = flip(.1)
var z = flip() ? a : c;
var b = z ? 'foo' : 'bar'
e)
var examFairPrior = Bernoulli({p: .8})
var doesHomeworkPrior = Bernoulli({p: .8})
var examFair = mem(function(exam) {return sample(examFairPrior)})
var doesHomework = mem(function(student) {return sample(doesHomeworkPrior)});
var pass = function(student, exam) {
return flip(examFair(exam) ?
(doesHomework(student) ? .9 : .5) :
(doesHomework(student) ? .2 : .1));
}
var a = pass('alice', 'historyExam');
var b = pass('bob', 'historyExam');