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/*
* File: BetaBinomialDistribution.java
* Authors: Kevin R. Dixon
* Company: Sandia National Laboratories
* Project: Cognitive Foundry
*
* Copyright Apr 11, 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.distribution;
import gov.sandia.cognition.annotation.PublicationReference;
import gov.sandia.cognition.annotation.PublicationType;
import gov.sandia.cognition.collection.IntegerSpan;
import gov.sandia.cognition.math.MathUtil;
import gov.sandia.cognition.math.UnivariateStatisticsUtil;
import gov.sandia.cognition.math.matrix.Vector;
import gov.sandia.cognition.math.matrix.VectorFactory;
import gov.sandia.cognition.statistics.AbstractClosedFormIntegerDistribution;
import gov.sandia.cognition.statistics.ClosedFormDiscreteUnivariateDistribution;
import gov.sandia.cognition.statistics.ClosedFormCumulativeDistributionFunction;
import gov.sandia.cognition.statistics.DistributionEstimator;
import gov.sandia.cognition.statistics.EstimableDistribution;
import gov.sandia.cognition.statistics.ProbabilityMassFunction;
import gov.sandia.cognition.statistics.ProbabilityMassFunctionUtil;
import gov.sandia.cognition.util.AbstractCloneableSerializable;
import gov.sandia.cognition.util.Pair;
import java.util.ArrayList;
import java.util.Collection;
import java.util.Random;
/**
* A Binomial distribution where the binomial parameter, p, is set according
* to a Beta distribution instead of a single value.
* @author Kevin R. Dixon
* @since 3.0
*/
@PublicationReference(
author="Eric Weisstein",
title="Beta Binomial Distribution",
type=PublicationType.WebPage,
year=2010,
url="http://mathworld.wolfram.com/BetaBinomialDistribution.html"
)
public class BetaBinomialDistribution
extends AbstractClosedFormIntegerDistribution
implements ClosedFormDiscreteUnivariateDistribution,
EstimableDistribution
{
/**
* Default shape, {@value}.
*/
public static final double DEFAULT_SHAPE = 1.0;
/**
* Default scale, {@value}.
*/
public static final double DEFAULT_SCALE = 1.0;
/**
* Default n, {@value}.
*/
public static final int DEFAULT_N = 1;
/**
* Number of observations, similar to the Binomial N,
* must be greater than zero
*/
protected int n;
/**
* Shape, similar to the beta parameter shape, must be greater than zero
*/
protected double shape;
/**
* Scale, similar to the beta parameter scale, must be greater than zero
*/
protected double scale;
/**
* Creates a new instance of BetaBinomialDistribution
*/
public BetaBinomialDistribution()
{
this( DEFAULT_N, DEFAULT_SHAPE, DEFAULT_SCALE );
}
/**
* Creates a new instance of BetaBinomialDistribution
* @param shape
* Shape, similar to the beta parameter shape, must be greater than zero
* @param scale
* Scale, similar to the beta parameter scale, must be greater than zero
* @param n
* Number of observations, similar to the Binomial N,
* must be greater than zero
*/
public BetaBinomialDistribution(
final int n,
final double shape,
final double scale )
{
this.setN(n);
this.setShape(shape);
this.setScale(scale);
}
/**
* Copy constructor
* @param other
* BetaBinomialDistribution to copy
*/
public BetaBinomialDistribution(
final BetaBinomialDistribution other )
{
this( other.getN(), other.getShape(), other.getScale() );
}
@Override
public BetaBinomialDistribution clone()
{
return (BetaBinomialDistribution) super.clone();
}
/**
* Getter for shape
* @return
* Shape, similar to the beta parameter shape, must be greater than zero
*/
public double getShape()
{
return this.shape;
}
/**
* Setter for shape
* @param shape
* Shape, similar to the beta parameter shape, must be greater than zero
*/
public void setShape(
final double shape)
{
if( shape <= 0.0 )
{
throw new IllegalArgumentException( "shape must be > 0.0" );
}
this.shape = shape;
}
/**
* Getter for scale
* @return
* Scale, similar to the beta parameter scale, must be greater than zero
*/
public double getScale()
{
return scale;
}
/**
* Setter for scale
* @param scale
* Scale, similar to the beta parameter scale, must be greater than zero
*/
public void setScale(
final double scale)
{
if( scale <= 0.0 )
{
throw new IllegalArgumentException( "scale must be > 0.0" );
}
this.scale = scale;
}
/**
* Getter for n
* @return
* Number of observations, similar to the Binomial N,
* must be greater than zero
*/
public int getN()
{
return this.n;
}
/**
* Setter for n
* @param n
* Number of observations, similar to the Binomial N,
* must be greater than zero
*/
public void setN(
final int n)
{
if( n < 1 )
{
throw new IllegalArgumentException( "n must be > 0" );
}
this.n = n;
}
@Override
public Number getMean()
{
return this.getMeanAsDouble();
}
@Override
public double getMeanAsDouble()
{
return this.n * this.shape / (this.shape+this.scale);
}
@Override
public void sampleInto(
final Random random,
final int sampleCount,
final Collection output)
{
ProbabilityMassFunctionUtil.sampleInto(
this.getProbabilityFunction(), random, sampleCount, output);
}
@Override
public int sampleAsInt(
final Random random)
{
// TODO: See if there is a way to do this without any boxing.
return ProbabilityMassFunctionUtil.sampleSingle(
this.getProbabilityFunction(), random).intValue();
}
@Override
public void sampleInto(
final Random random,
final int[] output,
final int start,
final int length)
{
// TODO: See if there is a way to do this without any boxing.
final ArrayList samples = this.sample(random, length);
for (int i = 0; i < length; i++)
{
output[start + i] = samples.get(i).intValue();
}
}
@Override
public BetaBinomialDistribution.CDF getCDF()
{
return new BetaBinomialDistribution.CDF( this );
}
@Override
public Vector convertToVector()
{
return VectorFactory.getDefault().copyValues(
this.n, this.shape, this.scale );
}
@Override
public void convertFromVector(
final Vector parameters)
{
parameters.assertDimensionalityEquals(3);
this.setN( (int) parameters.getElement(0) );
this.setShape(parameters.getElement(1) );
this.setScale(parameters.getElement(2) );
}
@Override
public Integer getMinSupport()
{
return 0;
}
@Override
public Integer getMaxSupport()
{
return this.n;
}
@Override
public double getVariance()
{
final double ss = this.shape + this.scale;
final double numer = this.n*this.shape*this.scale*(ss+this.n);
final double denom = ss*ss*(ss+1);
return numer / denom;
}
@Override
public IntegerSpan getDomain()
{
return new IntegerSpan(0, (int) Math.ceil(this.n) );
}
@Override
public int getDomainSize()
{
return ((int) Math.ceil(this.n)) + 1;
}
@Override
public BetaBinomialDistribution.PMF getProbabilityFunction()
{
return new BetaBinomialDistribution.PMF( this );
}
@Override
public BetaBinomialDistribution.MomentMatchingEstimator getEstimator()
{
return new BetaBinomialDistribution.MomentMatchingEstimator();
}
/**
* PMF of the BetaBinomialDistribution
*/
public static class PMF
extends BetaBinomialDistribution
implements ProbabilityMassFunction
{
/**
* Creates a new instance of BetaBinomialDistribution
*/
public PMF()
{
super();
}
/**
* Creates a new instance of BetaBinomialDistribution
* @param shape
* Shape, similar to the beta parameter shape, must be greater than zero
* @param scale
* Scale, similar to the beta parameter scale, must be greater than zero
* @param n
* Number of observations, similar to the Binomial N,
* must be greater than zero
*/
public PMF(
final int n,
final double shape,
final double scale )
{
super( n, shape, scale );
}
/**
* Copy constructor
* @param other
* BetaBinomialDistribution to copy
*/
public PMF(
final BetaBinomialDistribution other )
{
super( other );
}
@Override
public BetaBinomialDistribution.PMF getProbabilityFunction()
{
return this;
}
@Override
public Double evaluate(
final Number input)
{
return Math.exp( this.logEvaluate(input) );
}
@Override
public double logEvaluate(
final Number input)
{
if( input.doubleValue() < 0.0 )
{
return Math.log(0.0);
}
else if( input.doubleValue() > this.n )
{
return Math.log(0.0);
}
final int x = input.intValue();
double logSum = 0.0;
logSum += MathUtil.logBinomialCoefficient(this.n, x);
logSum -= MathUtil.logBetaFunction( this.shape, this.scale );
logSum += MathUtil.logBetaFunction( this.shape + x, this.n+this.scale - x);
return logSum;
}
@Override
public double getEntropy()
{
return ProbabilityMassFunctionUtil.getEntropy(this);
}
}
/**
* CDF of BetaBinomialDistribution
*/
public static class CDF
extends BetaBinomialDistribution
implements ClosedFormCumulativeDistributionFunction
{
/**
* Creates a new instance of BetaBinomialDistribution
*/
public CDF()
{
super();
}
/**
* Creates a new instance of BetaBinomialDistribution
* @param shape
* Shape, similar to the beta parameter shape, must be greater than zero
* @param scale
* Scale, similar to the beta parameter scale, must be greater than zero
* @param n
* Number of observations, similar to the Binomial N,
* must be greater than zero
*/
public CDF(
final int n,
final double shape,
final double scale )
{
super( n, shape, scale );
}
/**
* Copy constructor
* @param other
* BetaBinomialDistribution to copy
*/
public CDF(
final BetaBinomialDistribution other )
{
super( other );
}
@Override
public Double evaluate(
final Number input)
{
return ProbabilityMassFunctionUtil.computeCumulativeValue(
input.intValue(),this);
}
@Override
public BetaBinomialDistribution.CDF getCDF()
{
return this;
}
}
/**
* Estimates the parameters of a Beta-binomial distribution using the matching
* of moments, not maximum likelihood.
*/
@PublicationReference(
author={
"Ram C. Tripathi",
"Ramesh C. Gupta",
"John Gurland"
},
title="Estimation of parameters in the beta binomial model",
type=PublicationType.Journal,
publication="Annals of the Institute of Statistical Mathematics",
year=1994,
pages={317,331},
notes="Equation 2.11"
)
public static class MomentMatchingEstimator
extends AbstractCloneableSerializable
implements DistributionEstimator
{
/**
* Default constructor
*/
public MomentMatchingEstimator()
{
}
@Override
public BetaBinomialDistribution learn(
final Collection data)
{
Pair pair =
UnivariateStatisticsUtil.computeMeanAndVariance(data);
double mean = pair.getFirst();
double max = UnivariateStatisticsUtil.computeMaximum(data);
int N = (int) Math.ceil( max );
double eta = 0.0;
double smooth = 1.0;
for( Number value : data )
{
double numPositive = value.doubleValue() + smooth;
double numNegative = N - value.doubleValue() + smooth;
double e = numPositive / numNegative;
eta += e;
}
eta /= N;
double denom = N*mean - (N-mean)*eta;
double alpha = Math.abs( ((N-1) * eta * mean) / denom );
double beta = Math.abs( (N-1)*(N-mean)*eta / denom );
BetaBinomialDistribution.PMF distribution =
new BetaBinomialDistribution.PMF( N, alpha, beta );
return distribution;
}
/**
* Computes the Beta-Binomial distribution describes by the given moments
* @param N
* Number of trials
* @param mean
* Mean of the distribution
* @param variance
* Variance of the distribution
* @return
* Beta-Binomial distribution that has the same mean/variance as the
* given parameters.
*/
public static BetaBinomialDistribution.PMF learn(
final int N,
final double mean,
final double variance )
{
double denom = N*((variance/mean) - mean - 1.0) + mean;
double alpha = Math.abs((N*mean - variance) / denom);
double beta = Math.abs( (N-mean)*(N-(variance/mean)) / denom );
BetaBinomialDistribution.PMF distribution =
new BetaBinomialDistribution.PMF( N, alpha, beta );
return distribution;
}
}
}