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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.temporal;

import java.util.List;

import aima.core.probability.CategoricalDistribution;
import aima.core.probability.proposition.AssignmentProposition;

/**
 * Artificial Intelligence A Modern Approach (3rd Edition): page 576.

 * 

 * 
 * Generic interface for calling different implementations of the
 * forward-backward algorithm for smoothing: computing posterior probabilities
 * of a sequence of states given a sequence of observations.
 * 
 * 
 * @author Ciaran O'Reilly
 * 
 */
public interface ForwardBackwardInference extends ForwardStepInference,
		BackwardStepInference {

	/**
	 * The forward-backward algorithm for smoothing: computing posterior
	 * probabilities of a sequence of states given a sequence of observations.
	 * 
	 * @param ev
	 *            a vector of evidence values for steps 1,...,t
	 * @param prior
	 *            the prior distribution on the initial state,
	 *            P(X₀)
	 * @return a vector of smoothed estimates for steps 1,...,t
	 */
	List forwardBackward(
			List> ev, CategoricalDistribution prior);
}