aima.core.probability

Interface ProbabilityModel

All Known Subinterfaces:

FiniteProbabilityModel

All Known Implementing Classes:

FiniteBayesModel, FullJointDistributionBurglaryAlarmModel, FullJointDistributionMeningitisStiffNeckModel, FullJointDistributionModel, FullJointDistributionPairFairDiceModel, FullJointDistributionToothacheCavityCatchModel, FullJointDistributionToothacheCavityCatchWeatherModel

public interface ProbabilityModel

Artificial Intelligence A Modern Approach (3rd Edition): page 484.

A fully specified probability model associates a numerical probability P(ω) with each possible world. The set of all possible worlds is called the sample space Ω.

Author:

Ciaran O'Reilly

Field Summary

Fields

Modifier and Type	Field and Description
static double	DEFAULT_ROUNDING_THRESHOLD The default threshold for rounding errors.

Method Summary

Modifier and Type	Method and Description
java.util.Set<RandomVariable>	getRepresentation()
boolean	isValid()
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.
double	prior(Proposition... phi) For any proposition φ, P(φ) = ∑ω ∈ φ P(ω).

Field Detail

DEFAULT_ROUNDING_THRESHOLD

static final double DEFAULT_ROUNDING_THRESHOLD

The default threshold for rounding errors. Example, to test if probabilities sum to 1:

Math.abs(1 - probabilitySum) < ProbabilityModel.DEFAULT_ROUNDING_THRESHOLD;

See Also:

Constant Field Values

Method Detail

isValid

boolean isValid()

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

double prior(Proposition... phi)

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.

Parameters:

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

Returns:

the probability of the proposition φ.

posterior

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. 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

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

java.util.Set<RandomVariable> getRepresentation()

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.