aima.core.probability.full

Class FullJointDistributionModel

java.lang.Object

aima.core.probability.full.FullJointDistributionModel

All Implemented Interfaces:

FiniteProbabilityModel, ProbabilityModel

Direct Known Subclasses:

FullJointDistributionBurglaryAlarmModel, FullJointDistributionMeningitisStiffNeckModel, FullJointDistributionPairFairDiceModel, FullJointDistributionToothacheCavityCatchModel, FullJointDistributionToothacheCavityCatchWeatherModel

public class FullJointDistributionModel
extends java.lang.Object
implements FiniteProbabilityModel

An implementation of the FiniteProbabilityModel API using a full joint distribution as the underlying model.

Author:

Ciaran O'Reilly

Field Summary

Fields inherited from interface aima.core.probability.ProbabilityModel

DEFAULT_ROUNDING_THRESHOLD

Constructor Summary

Constructors

Constructor and Description
FullJointDistributionModel(double[] values, RandomVariable... vars)

Method Summary

Modifier and Type	Method and Description
java.util.Set<RandomVariable>	getRepresentation()
boolean	isValid()
CategoricalDistribution	jointDistribution(Proposition... propositions) Get a distribution on multiple variables.
double	posterior(Proposition phi, Proposition... evidence) Unlike unconditional or prior probabilities, most of the time we have some information, usually called evidence, that has already been revealed.
CategoricalDistribution	posteriorDistribution(Proposition phi, Proposition... evidence) Get a conditional distribution.
double	prior(Proposition... phi) For any proposition φ, P(φ) = ∑ω ∈ φ P(ω).
CategoricalDistribution	priorDistribution(Proposition... phi) P(X,...)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

FullJointDistributionModel

public FullJointDistributionModel(double[] values,
                                  RandomVariable... vars)

Method Detail

isValid

public boolean isValid()

Specified by:

isValid in interface ProbabilityModel

Returns:

true, if 0 <= P(ω) <= 1 for every ω and ∑_{ω ∈ Ω} P(ω) = 1 (Equation 13.1 pg. 484 AIMA3e), false otherwise.

prior

public double prior(Proposition... phi)

Description copied from interface: ProbabilityModel

For any proposition φ, P(φ) = ∑_{ω ∈ φ} P(ω). Refer to equation 13.2 page 485 of AIMA3e. Probabilities such as P(Total = 11) and P(doubles) are called unconditional or prior probabilities (and sometimes just "priors" for short); they refer to degrees of belief in propositions in the absence of any other information.

Specified by:

prior in interface ProbabilityModel

Parameters:

phi - the propositional terms for which a probability value is to be returned.

Returns:

the probability of the proposition φ.

posterior

public double posterior(Proposition phi,
                        Proposition... evidence)

Description copied from interface: ProbabilityModel

Unlike unconditional or prior probabilities, most of the time we have some information, usually called evidence, that has already been revealed. This is the conditional or posterior probability (or just "posterior" for short). Mathematically speaking, conditional probabilities are defined in terms of unconditional probabilities as follows, for any propositions a and b, we have:

P(a | b) = P(a AND b)/P(b)

which holds whenever P(b) > 0. Refer to equation 13.3 page 485 of AIMA3e. This can be rewritten in a different form called the product rule:

P(a AND b) = P(a | b)P(b)

and also as:

P(a AND b) = P(b | a)P(a)

whereby, equating the two right-hand sides and dividing by P(a) gives you Bayes' rule:

P(b | a) = (P(a | b)P(b))/P(a) - i.e. (likelihood * prior)/evidence

Specified by:

posterior in interface ProbabilityModel

Parameters:

phi - the proposition for which a probability value is to be returned.

evidence - information we already have.

Returns:

the probability of the proposition φ given evidence.

getRepresentation

public java.util.Set<RandomVariable> getRepresentation()

Specified by:

getRepresentation in interface ProbabilityModel

Returns:

a consistent ordered Set (e.g. LinkedHashSet) of the random variables describing the atomic variable/value pairs this probability model can take on. Refer to pg. 486 AIMA3e.

priorDistribution

public CategoricalDistribution priorDistribution(Proposition... phi)

Description copied from interface: FiniteProbabilityModel

P(X,...)

Specified by:

priorDistribution in interface FiniteProbabilityModel

Parameters:

phi - the propositions of interest.

Returns:

all the possible values of the propositions φ. This is a Vector of numbers, where we assume a predefined ordering of the domain of the relevant random variables.

posteriorDistribution

public CategoricalDistribution posteriorDistribution(Proposition phi,
                                                     Proposition... evidence)

Description copied from interface: FiniteProbabilityModel

Get a conditional distribution. Example:

P(X | Y) gives the values of P(X = x_i | Y = y_j) for each possible i, j pair.

Specified by:

posteriorDistribution in interface FiniteProbabilityModel

Parameters:

phi - the proposition for which a probability distribution is to be returned.

evidence - information we already have.

Returns:

the conditional distribution for P(φ | evidence).

jointDistribution

public CategoricalDistribution jointDistribution(Proposition... propositions)

Description copied from interface: FiniteProbabilityModel

Get a distribution on multiple variables. Example, the product rule:

P(X, Y) gives the values of P(X = x_i | Y = y_j)P(Y = y_j) for each possible i, j pair.

Specified by:

jointDistribution in interface FiniteProbabilityModel

Parameters:

propositions - the propositions for which a joint probability distribution is to be returned.

Returns:

the joint distribution for P(X, Y, ...).