four_dice.wppl

// 4 dice: 4, 6, 8 and 12 sides
// each dice is perfect
var dice = [
	Categorical(
		{
			ps: [1/4, 1/4, 1/4, 1/4],
			vs: [0, 1, 2, 3]
		}
	),
	Categorical(
		{
			ps: [1/6, 1/6, 1/6, 1/6, 1/6, 1/6],
			vs: [0, 1, 2, 3, 4, 5]
		}
	),
	Categorical(
		{
			ps: [1/8, 1/8, 1/8, 1/8, 1/8, 1/8, 1/8, 1/8],
			vs: [0, 1, 2, 3, 4, 5, 6, 7]
		}
	),
	Categorical(
		{
			ps: [1/12, 1/12, 1/12, 1/12, 1/12, 1/12, 1/12, 1/12, 1/12, 1/12, 1/12, 1/12],
			vs: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]
		}
	)
]

var model_1 = function() {
	// pick one of four dice
	var sel = sample(Categorical({ps: [1/4, 1/4, 1/4, 1/4], vs: [0, 1, 2, 3]}))

	// roll the picked dice twice
	var roll1 = sample(dice[sel])
	var roll2 = sample(dice[sel])

	// two rolls must return the same face
	condition(roll1 == roll2)

	// roll for the last time
	var roll3 = sample(dice[sel])

	condition(roll3 == roll2)

	// probability of third roll being the same as the first two
	return sel
}

var model_2 = function() {
	// pick one of four dice
	var sel = sample(Categorical({ps: [1/4, 1/4, 1/4, 1/4], vs: [0, 1, 2, 3]}))

	// roll the picked dice twice
	var roll1 = sample(dice[sel])
	var roll2 = sample(dice[sel])

	// two rolls must return the same face
	condition(roll1 == roll2)

	// roll for the last time
	var roll3 = sample(dice[sel])

	// prob that third roll is the same as the first two
	var same = (roll3 == roll2 && roll3 == roll1)

	return same
}

display("Probabilities selecting each dice:")
var posterior_1 = Infer({method: 'rejection', samples: 10000}, model_1)
display(posterior_1)

display("Probability of third roll same as the first two")
var posterior_2 = Infer({method: 'rejection', samples: 10000}, model_2)
display(posterior_2)