• ☰
  • Home
  • Introduction
  • Generative models
  • Conditioning
  • Causal and statistical dependence
  • Conditional dependence
  • Bayesian data analysis
  • Algorithms for inference
  • Rational process models
  • Learning as conditional inference
  • Learning with a language of thought
  • Hierarchical models
  • Occam's Razor
  • Learning (deep) continuous functions
  • Mixture models
  • Social cognition
  • Appendix - JavaScript basics
  • Appendix - Useful distributions

Exercise 1: Causal and statistical dependency.

For each of the following programs:

• Draw the dependency diagram (Bayes net). If you don’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');