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AIMA-Java Core Algorithms from the book Artificial Intelligence a Modern Approach 3rd Ed.

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package aima.core.probability;

import aima.core.probability.proposition.Proposition;

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

 * 

 * A probability model on a discrete, countable set of worlds. The proper
 * treatment of the continuous case brings in certain complications that are
 * less relevant for most purposes in AI.
 * 
 * @author Ciaran O'Reilly
 */
public interface FiniteProbabilityModel extends ProbabilityModel {

	/**
	 * P(X,...)

	 * 
	 * @param phi
	 *            the propositions of interest.
	 * @return 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.
	 */
	CategoricalDistribution priorDistribution(Proposition... phi);

	/**
	 * 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.
	 * 
	 * @param phi
	 *            the proposition for which a probability distribution is to be
	 *            returned.
	 * @param evidence
	 *            information we already have.
	 * @return the conditional distribution for P(φ | evidence).
	 */
	CategoricalDistribution posteriorDistribution(Proposition phi,
			Proposition... evidence);

	/**
	 * 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.
	 * 
	 * @param propositions
	 *            the propositions for which a joint probability distribution is
	 *            to be returned.
	 * @return the joint distribution for P(X, Y, ...).
	 */
	CategoricalDistribution jointDistribution(Proposition... propositions);
}