public double posterior(IProposition phi, params IProposition[] evidence)
{
IProposition conjEvidence = ProbUtil.constructConjunction(evidence);
// P(A | B) = P(A AND B)/P(B) - (13.3 AIMA3e)
IProposition aAndB = new ConjunctiveProposition(phi, conjEvidence);
double probabilityOfEvidence = prior(conjEvidence);
if (0 != probabilityOfEvidence)
{
return prior(aAndB)/probabilityOfEvidence;
}
return 0;
}
public double posterior(IProposition phi, params IProposition[] evidence)
{
IProposition conjEvidence = ProbUtil.constructConjunction(evidence);
// P(A | B) = P(A AND B)/P(B) - (13.3 AIMA3e)
IProposition aAndB = new ConjunctiveProposition(phi, conjEvidence);
double probabilityOfEvidence = prior(conjEvidence);
if (0 != probabilityOfEvidence)
{
return(prior(aAndB) / probabilityOfEvidence);
}
return(0);
}
// AIMA3e pg. 488, 494
protected void test_ToothacheCavityCatchWeatherModel(ProbabilityModel model)
{
// Should be able to run all the same queries for this independent
// sub model.
test_ToothacheCavityCatchModel(model);
// AIMA3e pg. 486
AssignmentProposition asunny = new AssignmentProposition(
ExampleRV.WEATHER_RV, "sunny");
AssignmentProposition arain = new AssignmentProposition(
ExampleRV.WEATHER_RV, "rain");
AssignmentProposition acloudy = new AssignmentProposition(
ExampleRV.WEATHER_RV, "cloudy");
AssignmentProposition asnow = new AssignmentProposition(
ExampleRV.WEATHER_RV, "snow");
Assert.AreEqual(0.6, model.prior(asunny), DELTA_THRESHOLD);
Assert(0.1, model.prior(arain), DELTA_THRESHOLD);
Assert.AreEqual(0.29, model.prior(acloudy), DELTA_THRESHOLD);
Assert.AreEqual(0.01, model.prior(asnow), DELTA_THRESHOLD);
// AIMA3e pg. 488
// P(sunny, cavity)
// P(sunny AND cavity)
AssignmentProposition atoothache = new AssignmentProposition(
ExampleRV.TOOTHACHE_RV, Boolean.TRUE);
AssignmentProposition acatch = new AssignmentProposition(
ExampleRV.CATCH_RV, Boolean.TRUE);
AssignmentProposition acavity = new AssignmentProposition(
ExampleRV.CAVITY_RV, Boolean.TRUE);
ConjunctiveProposition sunnyAndCavity = new ConjunctiveProposition(
asunny, acavity);
// 0.6 (sunny) * 0.2 (cavity) = 0.12
Assert.AreEqual(0.12, model.prior(asunny, acavity), DELTA_THRESHOLD);
Assert.AreEqual(0.12, model.prior(sunnyAndCavity), DELTA_THRESHOLD);
// AIMA3e pg. 494
// P(toothache, catch, cavity, cloudy) =
// P(cloudy | toothache, catch, cavity)P(toothache, catch, cavity)
Assert.AreEqual(
model.prior(atoothache, acatch, acavity, acloudy),
model.posterior(acloudy, atoothache, acatch, acavity)
* model.prior(atoothache, acatch, acavity),
DELTA_THRESHOLD);
ConjunctiveProposition toothacheAndCatchAndCavityAndCloudy = new ConjunctiveProposition(
new ConjunctiveProposition(atoothache, acatch),
new ConjunctiveProposition(acavity, acloudy));
ConjunctiveProposition toothacheAndCatchAndCavity = new ConjunctiveProposition(
new ConjunctiveProposition(atoothache, acatch), acavity);
Assert.AreEqual(
model.prior(toothacheAndCatchAndCavityAndCloudy),
model.posterior(acloudy, atoothache, acatch, acavity)
* model.prior(toothacheAndCatchAndCavity),
DELTA_THRESHOLD);
// P(cloudy | toothache, catch, cavity) = P(cloudy)
// (13.10)
Assert.AreEqual(
model.posterior(acloudy, atoothache, acatch, acavity),
model.prior(acloudy), DELTA_THRESHOLD);
// P(toothache, catch, cavity, cloudy) =
// P(cloudy)P(tootache, catch, cavity)
Assert.AreEqual(
model.prior(atoothache, acatch, acavity, acloudy),
model.prior(acloudy) * model.prior(atoothache, acatch, acavity),
DELTA_THRESHOLD);
// P(a | b) = P(a)
Assert.AreEqual(model.posterior(acavity, acloudy),
model.prior(acavity), DELTA_THRESHOLD);
// P(b | a) = P(b)
Assert.AreEqual(model.posterior(acloudy, acavity),
model.prior(acloudy), DELTA_THRESHOLD);
// P(a AND b) = P(a)P(b)
Assert.AreEqual(model.prior(acavity, acloudy), model.prior(acavity)
* model.prior(acloudy), DELTA_THRESHOLD);
ConjunctiveProposition acavityAndacloudy = new ConjunctiveProposition(
acavity, acloudy);
Assert.AreEqual(model.prior(acavityAndacloudy),
model.prior(acavity) * model.prior(acloudy), DELTA_THRESHOLD);
}
public void test_RollingPairFairDiceModel(ProbabilityModel model)
{
Assert.IsTrue(model.isValid());
// Ensure each dice has 1/6 probability
for (int d = 1; d <= 6; d++)
{
AssignmentProposition ad1 = new AssignmentProposition(
ExampleRV.DICE_1_RV, d);
AssignmentProposition ad2 = new AssignmentProposition(
ExampleRV.DICE_2_RV, d);
Assert.AreEqual(1.0 / 6.0, model.prior(ad1), DELTA_THRESHOLD);
Assert.AreEqual(1.0 / 6.0, model.prior(ad2), DELTA_THRESHOLD);
}
// Ensure each combination is 1/36
for (int d1 = 1; d1 <= 6; d1++)
{
for (int d2 = 1; d2 <= 6; d2++)
{
AssignmentProposition ad1 = new AssignmentProposition(
ExampleRV.DICE_1_RV, d1);
AssignmentProposition ad2 = new AssignmentProposition(
ExampleRV.DICE_2_RV, d2);
ConjunctiveProposition d1AndD2 = new ConjunctiveProposition(
ad1, ad2);
Assert.AreEqual(1.0 / 6.0, model.prior(ad1),
DELTA_THRESHOLD);
Assert.AreEqual(1.0 / 6.0, model.prior(ad2),
DELTA_THRESHOLD);
// pg. 485 AIMA3e
Assert.AreEqual(1.0 / 36.0, model.prior(ad1, ad2),
DELTA_THRESHOLD);
Assert.AreEqual(1.0 / 36.0, model.prior(d1AndD2),
DELTA_THRESHOLD);
Assert.AreEqual(1.0 / 6.0, model.posterior(ad1, ad2),
DELTA_THRESHOLD);
Assert.AreEqual(1.0 / 6.0, model.posterior(ad2, ad1),
DELTA_THRESHOLD);
}
}
// Test Sets of events defined via constraint propositions
IntegerSumProposition total11 = new IntegerSumProposition("Total11",
new FiniteIntegerDomain(11), ExampleRV.DICE_1_RV,
ExampleRV.DICE_2_RV);
Assert.AreEqual(2.0 / 36.0, model.prior(total11), DELTA_THRESHOLD);
EquivalentProposition doubles = new EquivalentProposition("Doubles",
ExampleRV.DICE_1_RV, ExampleRV.DICE_2_RV);
Assert.AreEqual(1.0 / 6.0, model.prior(doubles), DELTA_THRESHOLD);
SubsetProposition evenDice1 = new SubsetProposition("EvenDice1",
new FiniteIntegerDomain(2, 4, 6), ExampleRV.DICE_1_RV);
Assert.AreEqual(0.5, model.prior(evenDice1), DELTA_THRESHOLD);
SubsetProposition oddDice2 = new SubsetProposition("OddDice2",
new FiniteIntegerDomain(1, 3, 5), ExampleRV.DICE_2_RV);
Assert.AreEqual(0.5, model.prior(oddDice2), DELTA_THRESHOLD);
// pg. 485 AIMA3e
AssignmentProposition dice1Is5 = new AssignmentProposition(
ExampleRV.DICE_1_RV, 5);
Assert.AreEqual(1.0 / 6.0, model.posterior(doubles, dice1Is5),
DELTA_THRESHOLD);
Assert.AreEqual(1.0, model.prior(ExampleRV.DICE_1_RV),
DELTA_THRESHOLD);
Assert.AreEqual(1.0, model.prior(ExampleRV.DICE_2_RV),
DELTA_THRESHOLD);
Assert.AreEqual(1.0,
model.posterior(ExampleRV.DICE_1_RV, ExampleRV.DICE_2_RV),
DELTA_THRESHOLD);
Assert.AreEqual(1.0,
model.posterior(ExampleRV.DICE_2_RV, ExampleRV.DICE_1_RV),
DELTA_THRESHOLD);
// Test a disjunctive proposition pg.489
// P(a OR b) = P(a) + P(b) - P(a AND b)
// = 1/6 + 1/6 - 1/36
AssignmentProposition dice2Is5 = new AssignmentProposition(
ExampleRV.DICE_2_RV, 5);
DisjunctiveProposition dice1Is5OrDice2Is5 = new DisjunctiveProposition(
dice1Is5, dice2Is5);
Assert.AreEqual(1.0 / 6.0 + 1.0 / 6.0 - 1.0 / 36.0,
model.prior(dice1Is5OrDice2Is5), DELTA_THRESHOLD);
}
protected void test_ToothacheCavityCatchModel(ProbabilityModel model)
{
Assert.IsTrue(model.isValid());
AssignmentProposition atoothache = new AssignmentProposition(
ExampleRV.TOOTHACHE_RV, Boolean.TRUE);
AssignmentProposition anottoothache = new AssignmentProposition(
ExampleRV.TOOTHACHE_RV, Boolean.FALSE);
AssignmentProposition acavity = new AssignmentProposition(
ExampleRV.CAVITY_RV, Boolean.TRUE);
AssignmentProposition anotcavity = new AssignmentProposition(
ExampleRV.CAVITY_RV, Boolean.FALSE);
AssignmentProposition acatch = new AssignmentProposition(
ExampleRV.CATCH_RV, Boolean.TRUE);
AssignmentProposition anotcatch = new AssignmentProposition(
ExampleRV.CATCH_RV, Boolean.FALSE);
// AIMA3e pg. 485
Assert.AreEqual(0.2, model.prior(acavity), DELTA_THRESHOLD);
Assert.AreEqual(0.6, model.posterior(acavity, atoothache),
DELTA_THRESHOLD);
ConjunctiveProposition toothacheAndNotCavity = new ConjunctiveProposition(
atoothache, anotcavity);
Assert.AreEqual(0.0,
model.posterior(acavity, toothacheAndNotCavity),
DELTA_THRESHOLD);
Assert.AreEqual(0.0,
model.posterior(acavity, atoothache, anotcavity),
DELTA_THRESHOLD);
// AIMA3e pg. 492
DisjunctiveProposition cavityOrToothache = new DisjunctiveProposition(
acavity, atoothache);
Assert.AreEqual(0.28, model.prior(cavityOrToothache),
DELTA_THRESHOLD);
// AIMA3e pg. 493
Assert.AreEqual(0.4, model.posterior(anotcavity, atoothache),
DELTA_THRESHOLD);
Assert.AreEqual(1.0, model.prior(ExampleRV.TOOTHACHE_RV),
DELTA_THRESHOLD);
Assert.AreEqual(1.0, model.prior(ExampleRV.CAVITY_RV),
DELTA_THRESHOLD);
Assert.AreEqual(1.0, model.prior(ExampleRV.CATCH_RV),
DELTA_THRESHOLD);
Assert.AreEqual(1.0,
model.posterior(ExampleRV.TOOTHACHE_RV, ExampleRV.CAVITY_RV),
DELTA_THRESHOLD);
Assert.AreEqual(1.0,
model.posterior(ExampleRV.TOOTHACHE_RV, ExampleRV.CATCH_RV),
DELTA_THRESHOLD);
Assert.AreEqual(1.0, model.posterior(ExampleRV.TOOTHACHE_RV,
ExampleRV.CAVITY_RV, ExampleRV.CATCH_RV), DELTA_THRESHOLD);
Assert.AreEqual(1.0,
model.posterior(ExampleRV.CAVITY_RV, ExampleRV.TOOTHACHE_RV),
DELTA_THRESHOLD);
Assert.AreEqual(1.0,
model.posterior(ExampleRV.CAVITY_RV, ExampleRV.CATCH_RV),
DELTA_THRESHOLD);
Assert.AreEqual(1.0, model.posterior(ExampleRV.CAVITY_RV,
ExampleRV.TOOTHACHE_RV, ExampleRV.CATCH_RV), DELTA_THRESHOLD);
Assert.AreEqual(1.0,
model.posterior(ExampleRV.CATCH_RV, ExampleRV.CAVITY_RV),
DELTA_THRESHOLD);
Assert.AreEqual(1.0,
model.posterior(ExampleRV.CATCH_RV, ExampleRV.TOOTHACHE_RV),
DELTA_THRESHOLD);
Assert.AreEqual(1.0, model.posterior(ExampleRV.CATCH_RV,
ExampleRV.CAVITY_RV, ExampleRV.TOOTHACHE_RV), DELTA_THRESHOLD);
// AIMA3e pg. 495 - Bayes' Rule
// P(b|a) = P(a|b)P(b)/P(a)
Assert.AreEqual(model.posterior(acavity, atoothache),
(model.posterior(atoothache, acavity) * model.prior(acavity))
/ model.prior(atoothache), DELTA_THRESHOLD);
Assert.AreEqual(
model.posterior(acavity, anottoothache),
(model.posterior(anottoothache, acavity) * model.prior(acavity))
/ model.prior(anottoothache), DELTA_THRESHOLD);
Assert.AreEqual(
model.posterior(anotcavity, atoothache),
(model.posterior(atoothache, anotcavity) * model
.prior(anotcavity)) / model.prior(atoothache),
DELTA_THRESHOLD);
Assert.AreEqual(
model.posterior(anotcavity, anottoothache),
(model.posterior(anottoothache, anotcavity) * model
.prior(anotcavity)) / model.prior(anottoothache),
DELTA_THRESHOLD);
//
Assert.AreEqual(model.posterior(acavity, acatch),
(model.posterior(acatch, acavity) * model.prior(acavity))
/ model.prior(acatch), DELTA_THRESHOLD);
Assert.AreEqual(model.posterior(acavity, anotcatch),
(model.posterior(anotcatch, acavity) * model.prior(acavity))
/ model.prior(anotcatch), DELTA_THRESHOLD);
Assert.AreEqual(model.posterior(anotcavity, acatch),
(model.posterior(acatch, anotcavity) * model.prior(anotcavity))
/ model.prior(acatch), DELTA_THRESHOLD);
Assert.AreEqual(
model.posterior(anotcavity, anotcatch),
(model.posterior(anotcatch, anotcavity) * model
.prior(anotcavity)) / model.prior(anotcatch),
DELTA_THRESHOLD);
}
