/*
* File: UnivariateGaussianMeanVarianceBayesianEstimator.java
* Authors: Kevin R. Dixon
* Company: Sandia National Laboratories
* Project: Cognitive Foundry
*
* Copyright Mar 17, 2010, Sandia Corporation.
* Under the terms of Contract DE-AC04-94AL85000, there is a non-exclusive
* license for use of this work by or on behalf of the U.S. Government.
* Export of this program may require a license from the United States
* Government. See CopyrightHistory.txt for complete details.
*
*/
package gov.sandia.cognition.statistics.bayesian.conjugate;
import gov.sandia.cognition.annotation.PublicationReference;
import gov.sandia.cognition.annotation.PublicationReferences;
import gov.sandia.cognition.annotation.PublicationType;
import gov.sandia.cognition.collection.CollectionUtil;
import gov.sandia.cognition.math.matrix.Vector;
import gov.sandia.cognition.math.matrix.VectorFactory;
import gov.sandia.cognition.statistics.bayesian.AbstractBayesianParameter;
import gov.sandia.cognition.statistics.bayesian.BayesianParameter;
import gov.sandia.cognition.statistics.distribution.NormalInverseGammaDistribution;
import gov.sandia.cognition.statistics.distribution.StudentTDistribution;
import gov.sandia.cognition.statistics.distribution.UnivariateGaussian;
import java.util.ArrayList;
import java.util.Arrays;
/**
* Computes the mean and variance of a univariate Gaussian using the
* conjugate prior NormalInverseGammaDistribution
* @author Kevin R. Dixon
* @since 3.0
*/
@PublicationReferences(
references={
@PublicationReference(
author="Jeff Grynaviski",
title="Bayesian Analysis of the Normal Distribution, Part II",
type=PublicationType.Misc,
year=2009,
url="http://home.uchicago.edu/~grynav/bayes/ABSLec8.ppt"
)
,
@PublicationReference(
author="Wikipedia",
title="Conjugate Prior",
type=PublicationType.WebPage,
year=2009,
url="http://en.wikipedia.org/wiki/Conjugate_prior"
)
}
)
public class UnivariateGaussianMeanVarianceBayesianEstimator
extends AbstractConjugatePriorBayesianEstimator<Double,Vector,UnivariateGaussian,NormalInverseGammaDistribution>
implements ConjugatePriorBayesianEstimatorPredictor<Double,Vector,UnivariateGaussian,NormalInverseGammaDistribution>
{
/**
* Creates a new instance of UnivariateGaussianMeanVarianceBayesianEstimator
*/
public UnivariateGaussianMeanVarianceBayesianEstimator()
{
this( new NormalInverseGammaDistribution() );
}
/**
* Creates a new instance of UnivariateGaussianMeanVarianceBayesianEstimator
* @param prior
* Conjugate prior
*/
public UnivariateGaussianMeanVarianceBayesianEstimator(
NormalInverseGammaDistribution prior )
{
this( new UnivariateGaussian(), prior );
}
/**
* Creates a new instance of UnivariateGaussianMeanVarianceBayesianEstimator
* @param conditional
* Conditional distribution
* @param prior
* Conjugate prior
*/
public UnivariateGaussianMeanVarianceBayesianEstimator(
UnivariateGaussian conditional,
NormalInverseGammaDistribution prior )
{
this( new UnivariateGaussianMeanVarianceBayesianEstimator.Parameter(
conditional, prior) );
}
/**
* Creates a new instance of UnivariateGaussianMeanVarianceBayesianEstimator
* @param parameter
* Parameter that describes the relationship between the conditional and
* conjugate prior
*/
protected UnivariateGaussianMeanVarianceBayesianEstimator(
BayesianParameter<Vector,UnivariateGaussian,NormalInverseGammaDistribution> parameter )
{
super( parameter );
}
public UnivariateGaussianMeanVarianceBayesianEstimator.Parameter createParameter(
UnivariateGaussian conditional,
NormalInverseGammaDistribution prior)
{
return new UnivariateGaussianMeanVarianceBayesianEstimator.Parameter( conditional, prior );
}
public void update(
NormalInverseGammaDistribution target,
Double data)
{
this.update(target, Arrays.asList(data) );
}
@Override
public void update(
NormalInverseGammaDistribution prior,
Iterable<? extends Double> data )
{
ArrayList<? extends Double> dataArray = CollectionUtil.asArrayList(data);
final int n = dataArray.size();
double sum = 0.0;
double sum2 = 0.0;
for( Number x : data )
{
double v = x.doubleValue();
sum += v;
sum2 += v*v;
}
final double sampleMean = sum / n;
final double sampleVariance = (n*sum2 - sum*sum) / (n*n);
double lambda = prior.getLocation();
double nu = prior.getPrecision();
double alpha = prior.getShape();
double beta = prior.getScale();
double alphahat = alpha + n/2.0;
double nuhat = nu+n;
double lambdahat = (nu*lambda + sum) / nuhat;
double delta = sampleMean-lambda;
double betahat = beta + 0.5*n*sampleVariance + 0.5*((n*nu)/nuhat) * (delta*delta);
prior.setLocation(lambdahat);
prior.setPrecision(nuhat);
prior.setShape(alphahat);
prior.setScale(betahat);
}
public double computeEquivalentSampleSize(
NormalInverseGammaDistribution belief)
{
return belief.getPrecision();
}
public StudentTDistribution createPredictiveDistribution(
NormalInverseGammaDistribution posterior )
{
double mean = posterior.getLocation();
// double dofs = 2.0 * posterior.getShape();
double dofs = posterior.getPrecision();
double precision = posterior.getShape() / posterior.getScale();
return new StudentTDistribution( dofs, mean, precision );
}
/**
* Parameter for this conjugate prior estimator.
*/
public static class Parameter
extends AbstractBayesianParameter<Vector,UnivariateGaussian,NormalInverseGammaDistribution>
{
/**
* Name of the parameter, {@value}.
*/
public static final String NAME = "meanAndVariance";
/**
* Creates a new instance
* @param prior
* Default conjugate prior.
* @param conditional
* Conditional distribution of the conjugate prior.
*/
public Parameter(
UnivariateGaussian conditional,
NormalInverseGammaDistribution prior )
{
super( conditional, NAME, prior );
}
public void setValue(
Vector value)
{
value.assertDimensionalityEquals(2);
double mean = value.getElement(0);
double variance = value.getElement(1);
this.conditionalDistribution.setMean(mean);
this.conditionalDistribution.setVariance(variance);
}
public Vector getValue()
{
return VectorFactory.getDefault().copyValues(
this.conditionalDistribution.getMean(),
this.conditionalDistribution.getVariance() );
}
}
}