protected void test_ToothacheCavityCatchWeatherModel_Distributions(
IFiniteProbabilityModel model)
{
AssignmentProposition asunny = new AssignmentProposition(
ExampleRV.WEATHER_RV, "sunny");
AssignmentProposition acavity = new AssignmentProposition(
ExampleRV.CAVITY_RV, true);
// Should be able to run all the same queries for this independent
// sub model.
test_ToothacheCavityCatchModel_Distributions(model);
// AIMA3e pg. 487
// P(sunny, Cavity)
// Would be a two-element vector giving the probabilities of a sunny day
// with a cavity and a sunny day with no cavity.
assertArrayEquals(new double[] { 0.12, 0.48 }, model
.priorDistribution(asunny, ExampleRV.CAVITY_RV).getValues(),
DELTA_THRESHOLD);
// AIMA3e pg. 488 (i.e. one element Vector returned)
// P(sunny, cavity)
assertArrayEquals(new double[] { 0.12 }, model
.priorDistribution(asunny, acavity).getValues(),
DELTA_THRESHOLD);
// P(sunny AND cavity)
assertArrayEquals(new double[] { 0.12 }, model
.priorDistribution(new ConjunctiveProposition(asunny, acavity))
.getValues(), DELTA_THRESHOLD);
// P(sunny) = <0.6>
assertArrayEquals(new double[] { 0.6 },
model.priorDistribution(asunny).getValues(), DELTA_THRESHOLD);
}
//
// PROTECTED
//
protected void test_RollingPairFairDiceModel_Distributions(IFiniteProbabilityModel model)
{
AssignmentProposition ad1_1 = new AssignmentProposition(ExampleRV.DICE_1_RV, 1);
ICategoricalDistribution dD1_1 = model.priorDistribution(ad1_1);
assertArrayEquals(new double[] { 1.0 / 6.0 }, dD1_1.getValues(), DELTA_THRESHOLD);
ICategoricalDistribution dPriorDice1 = model.priorDistribution(ExampleRV.DICE_1_RV);
assertArrayEquals(new double[] { 1.0 / 6.0, 1.0 / 6.0, 1.0 / 6.0, 1.0 / 6.0, 1.0 / 6.0, 1.0 / 6.0 },
dPriorDice1.getValues(), DELTA_THRESHOLD);
ICategoricalDistribution dPriorDice2 = model.priorDistribution(ExampleRV.DICE_2_RV);
assertArrayEquals(new double[] { 1.0 / 6.0, 1.0 / 6.0, 1.0 / 6.0, 1.0 / 6.0, 1.0 / 6.0, 1.0 / 6.0 },
dPriorDice2.getValues(), DELTA_THRESHOLD);
ICategoricalDistribution dJointDice1Dice2 = model.jointDistribution(ExampleRV.DICE_1_RV, ExampleRV.DICE_2_RV);
Assert.AreEqual(36, dJointDice1Dice2.getValues().Length);
for (int i = 0; i < dJointDice1Dice2.getValues().Length; i++)
{
Assert.AreEqual(1.0 / 36.0, dJointDice1Dice2.getValues()[i], DELTA_THRESHOLD);
}
ICategoricalDistribution dJointDice2Dice1 = model.jointDistribution(ExampleRV.DICE_2_RV, ExampleRV.DICE_1_RV);
Assert.AreEqual(36, dJointDice2Dice1.getValues().Length);
for (int i = 0; i < dJointDice2Dice1.getValues().Length; i++)
{
Assert.AreEqual(1.0 / 36.0, dJointDice2Dice1.getValues()[i], DELTA_THRESHOLD);
}
//
// Test Sets of events
IntegerSumProposition total11 = new IntegerSumProposition("Total",
new FiniteIntegerDomain(11), ExampleRV.DICE_1_RV,
ExampleRV.DICE_2_RV);
// P<>(Total = 11) = <2.0/36.0>
assertArrayEquals(new double[] { 2.0 / 36.0 }, model.priorDistribution(total11).getValues(), DELTA_THRESHOLD);
// P<>(Dice1, Total = 11)
// = <0.0, 0.0, 0.0, 0.0, 1.0/36.0, 1.0/36.0>
assertArrayEquals(new double[] { 0, 0, 0, 0, 1.0 / 36.0, 1.0 / 36.0 },
model.priorDistribution(ExampleRV.DICE_1_RV, total11)
.getValues(), DELTA_THRESHOLD);
EquivalentProposition doubles = new EquivalentProposition("Doubles",
ExampleRV.DICE_1_RV, ExampleRV.DICE_2_RV);
// P(Doubles) = <1.0/6.0>
assertArrayEquals(new double[] { 1.0 / 6.0 }, model
.priorDistribution(doubles).getValues(), DELTA_THRESHOLD);
//
// Test posterior
//
// P<>(Dice1, Total = 11)
// = <0.0, 0.0, 0.0, 0.0, 0.5, 0.5>
assertArrayEquals(new double[] { 0, 0, 0, 0, 0.5, 0.5 }, model
.posteriorDistribution(ExampleRV.DICE_1_RV, total11)
.getValues(), DELTA_THRESHOLD);
// P<>(Dice1 | Doubles) = <1/6, 1/6, 1/6, 1/6, 1/6, 1/6>
assertArrayEquals(new double[] { 1.0 / 6.0, 1.0 / 6.0, 1.0 / 6.0, 1.0 / 6.0, 1.0 / 6.0, 1.0 / 6.0 }, model
.posteriorDistribution(ExampleRV.DICE_1_RV, doubles)
.getValues(), DELTA_THRESHOLD);
ICategoricalDistribution dPosteriorDice1GivenDice2 = model
.posteriorDistribution(ExampleRV.DICE_1_RV, ExampleRV.DICE_2_RV);
Assert.AreEqual(36, dPosteriorDice1GivenDice2.getValues().Length);
for (int i = 0; i < dPosteriorDice1GivenDice2.getValues().Length; i++)
{
Assert.AreEqual(1.0 / 6.0, dPosteriorDice1GivenDice2.getValues()[i], DELTA_THRESHOLD);
}
ICategoricalDistribution dPosteriorDice2GivenDice1 = model
.posteriorDistribution(ExampleRV.DICE_2_RV, ExampleRV.DICE_1_RV);
Assert.AreEqual(36, dPosteriorDice2GivenDice1.getValues().Length);
for (int i = 0; i < dPosteriorDice2GivenDice1.getValues().Length; i++)
{
Assert.AreEqual(1.0 / 6.0, dPosteriorDice2GivenDice1.getValues()[i], DELTA_THRESHOLD);
}
}
protected void test_ToothacheCavityCatchModel_Distributions(IFiniteProbabilityModel model)
{
AssignmentProposition atoothache = new AssignmentProposition(ExampleRV.TOOTHACHE_RV, true);
AssignmentProposition anottoothache = new AssignmentProposition(ExampleRV.TOOTHACHE_RV, false);
AssignmentProposition acatch = new AssignmentProposition(ExampleRV.CATCH_RV, true);
AssignmentProposition anotcatch = new AssignmentProposition(ExampleRV.CATCH_RV, false);
// AIMA3e pg. 493
// P<>(Cavity | toothache) = <0.6, 0.4>
assertArrayEquals(new double[] { 0.6, 0.4 }, model
.posteriorDistribution(ExampleRV.CAVITY_RV, atoothache)
.getValues(), DELTA_THRESHOLD);
// AIMA3e pg. 497
// P<>(Cavity | toothache AND catch) = <0.871, 0.129>
assertArrayEquals(new double[] { 0.8709677419354839, 0.12903225806451615 },
model.posteriorDistribution(ExampleRV.CAVITY_RV, atoothache,
acatch).getValues(), DELTA_THRESHOLD);
// AIMA3e pg. 498
// (13.17)
// P<>(toothache AND catch | Cavity)
// = P<>(toothache | Cavity)P<>(catch | Cavity)
ConjunctiveProposition toothacheAndCatch = new ConjunctiveProposition(atoothache, acatch);
assertArrayEquals(model.posteriorDistribution(toothacheAndCatch,
ExampleRV.CAVITY_RV).getValues(),
model.posteriorDistribution(atoothache, ExampleRV.CAVITY_RV)
.multiplyBy(
model.posteriorDistribution(acatch,
ExampleRV.CAVITY_RV)).getValues(),
DELTA_THRESHOLD);
// (13.18)
// P<>(Cavity | toothache AND catch)
// = αP<>(toothache | Cavity)P<>(catch | Cavity)P(Cavity)
assertArrayEquals(model.posteriorDistribution(ExampleRV.CAVITY_RV,
toothacheAndCatch).getValues(),
model.posteriorDistribution(atoothache, ExampleRV.CAVITY_RV)
.multiplyBy(
model.posteriorDistribution(acatch,
ExampleRV.CAVITY_RV))
.multiplyBy(
model.priorDistribution(ExampleRV.CAVITY_RV))
.normalize().getValues(), DELTA_THRESHOLD);
// (13.19)
// P<>(Toothache, Catch | Cavity)
// = P<>(Toothache | Cavity)P<>(Catch | Cavity)
ConjunctiveProposition toothacheAndCatchRV = new ConjunctiveProposition(ExampleRV.TOOTHACHE_RV, ExampleRV.CATCH_RV);
assertArrayEquals(model.posteriorDistribution(toothacheAndCatchRV,
ExampleRV.CAVITY_RV).getValues(),
model.posteriorDistribution(ExampleRV.TOOTHACHE_RV,
ExampleRV.CAVITY_RV)
.multiplyByPOS(
model.posteriorDistribution(ExampleRV.CATCH_RV,
ExampleRV.CAVITY_RV),
ExampleRV.TOOTHACHE_RV, ExampleRV.CATCH_RV,
ExampleRV.CAVITY_RV).getValues(),
DELTA_THRESHOLD);
// (product rule)
// P<>(Toothache, Catch, Cavity)
// = P<>(Toothache, Catch | Cavity)P<>(Cavity)
assertArrayEquals(model.priorDistribution(ExampleRV.TOOTHACHE_RV,
ExampleRV.CATCH_RV, ExampleRV.CAVITY_RV).getValues(),
model.posteriorDistribution(toothacheAndCatchRV,
ExampleRV.CAVITY_RV)
.multiplyBy(
model.priorDistribution(ExampleRV.CAVITY_RV))
.getValues(), DELTA_THRESHOLD);
// (using 13.19)
// P<>(Toothache, Catch | Cavity)P<>(Cavity)
// = P<>(Toothache | Cavity)P<>(Catch | Cavity)P<>(Cavity)
assertArrayEquals(model.posteriorDistribution(toothacheAndCatchRV,
ExampleRV.CAVITY_RV)
.multiplyBy(
model.priorDistribution(ExampleRV.CAVITY_RV))
.getValues(),
model.posteriorDistribution(ExampleRV.TOOTHACHE_RV,
ExampleRV.CAVITY_RV)
.multiplyByPOS(
model.posteriorDistribution(ExampleRV.CATCH_RV,
ExampleRV.CAVITY_RV)
.multiplyBy(
model.priorDistribution(ExampleRV.CAVITY_RV)),
ExampleRV.TOOTHACHE_RV, ExampleRV.CATCH_RV,
ExampleRV.CAVITY_RV).getValues(),
DELTA_THRESHOLD);
//
// P<>(Toothache, Catch, Cavity)
// = P<>(Toothache | Cavity)P<>(Catch | Cavity)P<>(Cavity)
assertArrayEquals(model.priorDistribution(ExampleRV.TOOTHACHE_RV,
ExampleRV.CATCH_RV, ExampleRV.CAVITY_RV).getValues(),
model.posteriorDistribution(ExampleRV.TOOTHACHE_RV,
ExampleRV.CAVITY_RV)
.multiplyByPOS(
model.posteriorDistribution(ExampleRV.CATCH_RV,
ExampleRV.CAVITY_RV),
ExampleRV.TOOTHACHE_RV, ExampleRV.CATCH_RV,
ExampleRV.CAVITY_RV)
.multiplyBy(
model.priorDistribution(ExampleRV.CAVITY_RV))
.getValues(), DELTA_THRESHOLD);
// AIMA3e pg. 496
// General case of Bayes' Rule
// P<>(Y | X) = P<>(X | Y)P<>(Y)/P<>(X)
// Note: Performing in this order -
// P<>(Y | X) = (P<>(Y)P<>(X | Y))/P<>(X)
// as default multiplication of distributions are not commutative (could
// also use pointwiseProductPOS() to specify the order).
assertArrayEquals(model.posteriorDistribution(ExampleRV.CAVITY_RV,
ExampleRV.TOOTHACHE_RV).getValues(),
model.priorDistribution(ExampleRV.CAVITY_RV)
.multiplyBy(
model.posteriorDistribution(
ExampleRV.TOOTHACHE_RV,
ExampleRV.CAVITY_RV))
.divideBy(
model.priorDistribution(ExampleRV.TOOTHACHE_RV))
.getValues(), DELTA_THRESHOLD);
assertArrayEquals(
model.posteriorDistribution(ExampleRV.CAVITY_RV,
ExampleRV.CATCH_RV).getValues(),
model.priorDistribution(ExampleRV.CAVITY_RV)
.multiplyBy(
model.posteriorDistribution(ExampleRV.CATCH_RV,
ExampleRV.CAVITY_RV))
.divideBy(model.priorDistribution(ExampleRV.CATCH_RV))
.getValues(), DELTA_THRESHOLD);
// General Bayes' Rule conditionalized on background evidence e (13.3)
// P<>(Y | X, e) = P<>(X | Y, e)P<>(Y|e)/P<>(X | e)
// Note: Performing in this order -
// P<>(Y | X, e) = (P<>(Y|e)P<>(X | Y, e)))/P<>(X | e)
// as default multiplication of distributions are not commutative (could
// also use pointwiseProductPOS() to specify the order).
assertArrayEquals(
model.posteriorDistribution(ExampleRV.CAVITY_RV,
ExampleRV.TOOTHACHE_RV, acatch).getValues(),
model.posteriorDistribution(ExampleRV.CAVITY_RV, acatch)
.multiplyBy(
model.posteriorDistribution(
ExampleRV.TOOTHACHE_RV,
ExampleRV.CAVITY_RV, acatch))
.divideBy(
model.posteriorDistribution(
ExampleRV.TOOTHACHE_RV, acatch))
.getValues(), DELTA_THRESHOLD);
//
assertArrayEquals(
model.posteriorDistribution(ExampleRV.CAVITY_RV,
ExampleRV.TOOTHACHE_RV, anotcatch).getValues(),
model.posteriorDistribution(ExampleRV.CAVITY_RV, anotcatch)
.multiplyBy(
model.posteriorDistribution(
ExampleRV.TOOTHACHE_RV,
ExampleRV.CAVITY_RV, anotcatch))
.divideBy(
model.posteriorDistribution(
ExampleRV.TOOTHACHE_RV, anotcatch))
.getValues(), DELTA_THRESHOLD);
//
assertArrayEquals(
model.posteriorDistribution(ExampleRV.CAVITY_RV,
ExampleRV.CATCH_RV, atoothache).getValues(),
model.posteriorDistribution(ExampleRV.CAVITY_RV, atoothache)
.multiplyBy(
model.posteriorDistribution(ExampleRV.CATCH_RV,
ExampleRV.CAVITY_RV, atoothache))
.divideBy(
model.posteriorDistribution(ExampleRV.CATCH_RV,
atoothache)).getValues(),
DELTA_THRESHOLD);
assertArrayEquals(
model.posteriorDistribution(ExampleRV.CAVITY_RV,
ExampleRV.CATCH_RV, anottoothache).getValues(),
model.posteriorDistribution(ExampleRV.CAVITY_RV, anottoothache)
.multiplyBy(
model.posteriorDistribution(ExampleRV.CATCH_RV,
ExampleRV.CAVITY_RV, anottoothache))
.divideBy(
model.posteriorDistribution(ExampleRV.CATCH_RV,
anottoothache)).getValues(),
DELTA_THRESHOLD);
}