beast.math.distributions.BetaDistribution.java Source code

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/*
 * BetaDistribution.java
 *
 * BEAST: Bayesian Evolutionary Analysis by Sampling Trees
 * Copyright (C) 2014 BEAST Developers
 *
 * BEAST is free software: you can redistribute it and/or modify it
 * under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License,
 * or (at your option) any later version.
 *
 * BEAST is distributed in the hope that it will be useful, but
 * WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with BEAST.  If not, see <http://www.gnu.org/licenses/>.
 */

package beast.math.distributions;

import beast.math.UnivariateFunction;
import org.apache.commons.math3.special.Beta;
import org.apache.commons.math3.special.Gamma;

/**
 * User: dkuh004
 * Date: Mar 25, 2011
 * Time: 11:32:25 AM
 */
public class BetaDistribution implements Distribution {

    // Default inverse cumulative probability accurac
    public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY = 1e-9;

    // first shape parameter
    private double alpha;

    // second shape parameter
    private double beta;

    // Normalizing factor used in density computations. updated whenever alpha or beta are changed.
    private double z;

    // Inverse cumulative probability accuracy
    private final double solverAbsoluteAccuracy;

    /**
     * This general constructor creates a new beta distribution with a
     * specified mean and scale
     *
     * @param alpha   shape parameter
     * @param beta    shape parameter
     */
    public BetaDistribution(double alpha, double beta) {
        this.alpha = alpha;
        this.beta = beta;
        z = Double.NaN;
        solverAbsoluteAccuracy = DEFAULT_INVERSE_ABSOLUTE_ACCURACY;
    }

    public double getAlpha() {
        return alpha;
    }

    public double getBeta() {
        return beta;
    }

    // Recompute the normalization factor.
    private void recomputeZ() {
        if (Double.isNaN(z)) {
            z = Gamma.logGamma(alpha) + Gamma.logGamma(beta) - Gamma.logGamma(alpha + beta);
        }
    }

    /**
     * probability density function of the distribution
     *
     * @param x argument
     * @return pdf value
     */
    public double pdf(double x) {
        recomputeZ();
        if (x < 0 || x > 1) {
            return 0;
        } else if (x == 0) {
            if (alpha < 1) {
                // AR - throwing exceptions deep in numerical code causes trouble. Catching runtime
                // exceptions is bad. Better to return NaN and let the calling code deal with it.
                return Double.NaN;
                //                throw MathRuntimeException.createIllegalArgumentException(
                //                        "Cannot compute beta density at 0 when alpha = {0,number}", alpha);
            }
            return 0;
        } else if (x == 1) {
            if (beta < 1) {
                // AR - throwing exceptions deep in numerical code causes trouble. Catching runtime
                // exceptions is bad. Better to return NaN and let the calling code deal with it.
                return Double.NaN;
                //                throw MathRuntimeException.createIllegalArgumentException(
                //                        "Cannot compute beta density at 1 when beta = %.3g", beta);
            }
            return 0;
        } else {
            double logX = Math.log(x);
            double log1mX = Math.log1p(-x);
            return Math.exp((alpha - 1) * logX + (beta - 1) * log1mX - z);
        }
    }

    /**
     * the natural log of the probability density function of the distribution
     *
     * @param x argument
     * @return log pdf value
     */
    public double logPdf(double x) {
        recomputeZ();
        if (x < 0 || x > 1) {
            return 0;
        } else if (x == 0) {
            if (alpha < 1) {
                // AR - throwing exceptions deep in numerical code causes trouble. Catching runtime
                // exceptions is bad. Better to return NaN and let the calling code deal with it.
                return Double.NaN;
                //                throw MathRuntimeException.createIllegalArgumentException(
                //                        "Cannot compute beta density at 0 when alpha = {0,number}", alpha);
            }
            return 0;
        } else if (x == 1) {
            if (beta < 1) {
                // AR - throwing exceptions deep in numerical code causes trouble. Catching runtime
                // exceptions is bad. Better to return NaN and let the calling code deal with it.
                return Double.NaN;
                //                throw MathRuntimeException.createIllegalArgumentException(
                //                        "Cannot compute beta density at 1 when beta = %.3g", beta);
            }
            return 0;
        } else {
            double logX = Math.log(x);
            double log1mX = Math.log1p(-x);
            return (alpha - 1) * logX + (beta - 1) * log1mX - z;
        }
    }

    /**
     * quantile (inverse cumulative density function) of the distribution
     *
     * @param y argument
     * @return icdf value
     */
    public double quantile(double y) {
        if (y == 0) {
            return 0;
        } else if (y == 1) {
            return 1;
        } else {
            throw new RuntimeException();
            //            try{
            //                return super.inverseCumulativeProbability(y);
            //            } catch (MathException e) {
            ////                throw MathRuntimeException.createIllegalArgumentException(                // AR - throwing exceptions deep in numerical code causes trouble. Catching runtime
            //                // exceptions is bad. Better to return NaN and let the calling code deal with it.
            //                return Double.NaN;
            //
            ////                    "Couldn't calculate beta quantile for alpha = " + alpha + ", beta = " + beta + ": " +e.getMessage());
            //            }
        }
    }

    protected double getInitialDomain(double p) {
        return p;
    }

    protected double getDomainLowerBound(double p) {
        return 0;
    }

    protected double getDomainUpperBound(double p) {
        return 1;
    }

    public double cdf(double x) {
        if (x <= 0) {
            return 0;
        } else if (x >= 1) {
            return 1;
        } else {
            return Beta.regularizedBeta(x, alpha, beta);
        }

    }

    public double cumulativeProbability(double x) {
        if (x <= 0) {
            return 0;
        } else if (x >= 1) {
            return 1;
        } else {
            return Beta.regularizedBeta(x, alpha, beta);
        }
    }

    public double cumulativeProbability(double x0, double x1) {
        return cumulativeProbability(x1) - cumulativeProbability(x0);
    }

    //Return the absolute accuracy setting of the solver used to estimate inverse cumulative probabilities.
    protected double getSolverAbsoluteAccuracy() {
        return solverAbsoluteAccuracy;
    }

    /**
     * cumulative density function of the distribution
     *
     * @param x argument
     * @return cdf value
     */
    //    public double cdf(double x){
    //        throw new UnsupportedOperationException();
    //    }

    /**
     * mean of the distribution
     *
     * @return mean
     */
    public double mean() {
        return (alpha / (alpha + beta));
    }

    /**
     * variance of the distribution
     *
     * @return variance
     */
    public double variance() {
        return (alpha * beta) / ((alpha + beta) * (alpha + beta) * (alpha + beta + 1));
    }

    /**
     * @return a probability density function representing this distribution
     */
    public final UnivariateFunction getProbabilityDensityFunction() {
        return pdfFunction;
    }

    private final UnivariateFunction pdfFunction = new UnivariateFunction() {
        public final double evaluate(double x) {
            return pdf(x);
        }

        public final double getLowerBound() {
            return 0.0;
        }

        public final double getUpperBound() {
            return 1.0;
        }
    };

}