mathnet-numerics/src/Numerics/Distributions/Multivariate/NormalGamma.cs

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namespace MathNet.Numerics.Distributions
{
    using System;
    using System.Collections.Generic;
    using Properties;

    /// <summary>
    /// This structure represents the type over which the <see cref="NormalGamma"/> distribution
    /// is defined.
    /// </summary>
    public struct MeanPrecisionPair
    {
        /// <summary>
        /// The mean value.
        /// </summary>
        double _mean;

        /// <summary>
        /// The precision value.
        /// </summary>
        double _precision;

        /// <summary>
        /// Initializes a new instance of the <see cref="MeanPrecisionPair"/> struct. 
        /// </summary>
        /// <param name="m">The mean of the pair.</param>
        /// <param name="p">The precision of the pair.</param>
        public MeanPrecisionPair(double m, double p)
        {
            _mean = m;
            _precision = p;
        }

        /// <summary>
        /// Gets or sets the mean of the pair.
        /// </summary>
        public double Mean
        {
            get { return _mean; }

            set { _mean = value; }
        }

        /// <summary>
        /// Gets or sets the precision of the pair.
        /// </summary>
        public double Precision
        {
            get { return _precision; }

            set { _precision = value; }
        }
    }

    /// <summary>
    /// <para>The <see cref="NormalGamma"/> distribution is the conjugate prior distribution for the <see cref="Normal"/>
    /// distribution. It specifies a prior over the mean and precision of the <see cref="Normal"/> distribution.</para>
    /// <para>It is parameterized by four numbers: the mean location, the mean scale, the precision shape and the
    /// precision inverse scale.</para>
    /// <para>The distribution NG(mu, tau | mloc,mscale,psscale,pinvscale) = Normal(mu | mloc, 1/(mscale*tau)) * Gamma(tau | psscale,pinvscale).</para>
    /// <para>The following degenerate cases are special: when the precision is known,
    /// the precision shape will encode the value of the precision while the precision inverse scale is positive
    /// infinity. When the mean is known, the mean location will encode the value of the mean while the scale
    /// will be positive infinity. A completely degenerate NormalGamma distribution with known mean and precision is possible as well.</para>
    /// <a href="http://en.wikipedia.org/wiki/Normal-gamma_distribution">Wikipedia - Normal-Gamma distribution</a>.
    /// </summary>
    /// <remarks><para>The distribution will use the <see cref="System.Random"/> by default. 
    /// Users can get/set the random number generator by using the <see cref="RandomSource"/> property.</para>
    /// <para>The statistics classes will check all the incoming parameters whether they are in the allowed
    /// range. This might involve heavy computation. Optionally, by setting Control.CheckDistributionParameters
    /// to <c>false</c>, all parameter checks can be turned off.</para></remarks>
    public class NormalGamma
    {
        /// <summary>
        /// The location of the mean.
        /// </summary>
        double _meanLocation;

        /// <summary>
        /// The scale of the mean.
        /// </summary>
        double _meanScale;

        /// <summary>
        /// The shape of the precision.
        /// </summary>
        double _precisionShape;

        /// <summary>
        /// The inverse scale of the precision.
        /// </summary>
        double _precisionInvScale;

        /// <summary>
        /// The distribution's random number generator.
        /// </summary>
        Random _random;

        /// <summary>
        /// Initializes a new instance of the <see cref="NormalGamma"/> class. 
        /// </summary>
        /// <param name="meanLocation">The location of the mean.</param>
        /// <param name="meanScale">The scale of the mean.</param>
        /// <param name="precisionShape">The shape of the precision.</param>
        /// <param name="precisionInverseScale">The inverse scale of the precision.</param>
        public NormalGamma(double meanLocation, double meanScale, double precisionShape, double precisionInverseScale)
        {
            _random = new Random();
            SetParameters(meanLocation, meanScale, precisionShape, precisionInverseScale);
        }

        /// <summary>
        /// Initializes a new instance of the <see cref="NormalGamma"/> class. 
        /// </summary>
        /// <param name="meanLocation">The location of the mean.</param>
        /// <param name="meanScale">The scale of the mean.</param>
        /// <param name="precisionShape">The shape of the precision.</param>
        /// <param name="precisionInverseScale">The inverse scale of the precision.</param>
        /// <param name="randomSource">The random number generator which is used to draw random samples.</param>
        public NormalGamma(double meanLocation, double meanScale, double precisionShape, double precisionInverseScale, Random randomSource)
        {
            _random = randomSource ?? new Random();
            SetParameters(meanLocation, meanScale, precisionShape, precisionInverseScale);
        }

        /// <summary>
        /// Checks whether the parameters of the distribution are valid. 
        /// </summary>
        /// <param name="meanLocation">The location of the mean.</param>
        /// <param name="meanScale">The scale of the mean.</param>
        /// <param name="precShape">The shape of the precision.</param>
        /// <param name="precInvScale">The inverse scale of the precision.</param>
        /// <returns><c>true</c> when the parameters are valid, <c>false</c> otherwise.</returns>
        static bool IsValidParameterSet(double meanLocation, double meanScale, double precShape, double precInvScale)
        {
            return (meanScale > 0.0) && (precShape > 0.0) && (precInvScale > 0.0) && !Double.IsNaN(meanLocation);
        }

        /// <summary>
        /// Sets the parameters of the distribution after checking their validity.
        /// </summary>
        /// <param name="meanLocation">The location of the mean.</param>
        /// <param name="meanScale">The scale of the mean.</param>
        /// <param name="precShape">The shape of the precision.</param>
        /// <param name="precInvScale">The inverse scale of the precision.</param>
        /// <exception cref="ArgumentOutOfRangeException">When the parameters don't pass the <see cref="IsValidParameterSet"/> function.</exception>
        void SetParameters(double meanLocation, double meanScale, double precShape, double precInvScale)
        {
            if (Control.CheckDistributionParameters && !IsValidParameterSet(meanLocation, meanScale, precShape, precInvScale))
            {
                throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
            }

            _meanLocation = meanLocation;
            _meanScale = meanScale;
            _precisionShape = precShape;
            _precisionInvScale = precInvScale;
        }

        /// <summary>
        /// A string representation of the distribution.
        /// </summary>
        /// <returns>a string representation of the distribution.</returns>
        public override string ToString()
        {
            return "NormalGamma(Mean Location = " + _meanLocation + ", Mean Scale = " + _meanScale +
                ", Precision Shape = " + _precisionShape + ", Precision Inverse Scale = " + _precisionInvScale + ")";
        }

        /// <summary>
        /// Gets or sets the location of the mean.
        /// </summary>
        public double MeanLocation
        {
            get { return _meanLocation; }
            set { SetParameters(value, _meanScale, _precisionShape, _precisionInvScale); }
        }

        /// <summary>
        /// Gets or sets the scale of the mean.
        /// </summary>
        public double MeanScale
        {
            get { return _meanScale; }
            set { SetParameters(_meanLocation, value, _precisionShape, _precisionInvScale); }
        }

        /// <summary>
        /// Gets or sets the shape of the precision.
        /// </summary>
        public double PrecisionShape
        {
            get { return _precisionShape; }
            set { SetParameters(_meanLocation, _meanScale, value, _precisionInvScale); }
        }

        /// <summary>
        /// Gets or sets the inverse scale of the precision.
        /// </summary>
        public double PrecisionInverseScale
        {
            get { return _precisionInvScale; }
            set { SetParameters(_meanLocation, _meanScale, _precisionShape, value); }
        }

        /// <summary>
        /// Gets or sets the random number generator which is used to draw random samples.
        /// </summary>
        public Random RandomSource
        {
            get { return _random; }
            set
            {
                if (value == null)
                {
                    throw new ArgumentNullException();
                }

                _random = value;
            }
        }

        /// <summary>
        /// Returns the marginal distribution for the mean of the <c>NormalGamma</c> distribution.
        /// </summary>
        /// <returns>the marginal distribution for the mean of the <c>NormalGamma</c> distribution.</returns>
        public StudentT MeanMarginal()
        {
            if (Double.IsPositiveInfinity(_precisionInvScale))
            {
                return new StudentT(_meanLocation, 1.0/(_meanScale*_precisionShape), Double.PositiveInfinity);
            }

            return new StudentT(_meanLocation, Math.Sqrt(_precisionInvScale/(_meanScale*_precisionShape)), 2.0*_precisionShape);
        }

        /// <summary>
        /// Returns the marginal distribution for the precision of the <see cref="NormalGamma"/> distribution.
        /// </summary>
        /// <returns>The marginal distribution for the precision of the <see cref="NormalGamma"/> distribution/</returns>
        public Gamma PrecisionMarginal()
        {
            return new Gamma(_precisionShape, _precisionInvScale);
        }

        /// <summary>
        /// Gets the mean of the distribution.
        /// </summary>
        /// <value>The mean of the distribution.</value>
        public MeanPrecisionPair Mean
        {
            get { return Double.IsPositiveInfinity(_precisionInvScale) ? new MeanPrecisionPair(_meanLocation, _precisionShape) : new MeanPrecisionPair(_meanLocation, _precisionShape/_precisionInvScale); }
        }

        /// <summary>
        /// Gets the variance of the distribution.
        /// </summary>
        /// <value>The mean of the distribution.</value>
        public MeanPrecisionPair Variance
        {
            get { return new MeanPrecisionPair(_precisionInvScale/(_meanScale*(_precisionShape - 1)), _precisionShape/Math.Sqrt(_precisionInvScale)); }
        }

        /// <summary>
        /// Evaluates the probability density function for a NormalGamma distribution.
        /// </summary>
        /// <param name="mp">The mean/precision pair of the distribution</param>
        /// <returns>Density value</returns>
        public double Density(MeanPrecisionPair mp)
        {
            return Density(mp.Mean, mp.Precision);
        }

        /// <summary>
        /// Evaluates the probability density function for a NormalGamma distribution.
        /// </summary>
        /// <param name="mean">The mean of the distribution</param>
        /// <param name="prec">The precision of the distribution</param>
        /// <returns>Density value</returns>
        public double Density(double mean, double prec)
        {
            if (Double.IsPositiveInfinity(_precisionInvScale) && _meanScale == 0.0)
            {
                throw new NotSupportedException();
            }

            if (Double.IsPositiveInfinity(_precisionInvScale))
            {
                throw new NotSupportedException();
            }

            if (_meanScale <= 0.0)
            {
                throw new NotSupportedException();
            }

            // double e = -0.5 * prec * (mean - _meanLocation) * (mean - _meanLocation) - prec * _precisionInvScale;
            // return Math.Pow(prec * _precisionInvScale, _precisionShape) * Math.Exp(e) / (Constants.Sqrt2Pi * Math.Sqrt(prec) * SpecialFunctions.Gamma(_precisionShape));
            double e = -(0.5*prec*_meanScale*(mean - _meanLocation)*(mean - _meanLocation)) - (prec*_precisionInvScale);
            return Math.Pow(prec*_precisionInvScale, _precisionShape)*Math.Exp(e)*Math.Sqrt(_meanScale)
                /(Constants.Sqrt2Pi*Math.Sqrt(prec)*SpecialFunctions.Gamma(_precisionShape));
        }

        /// <summary>
        /// Evaluates the log probability density function for a NormalGamma distribution.
        /// </summary>
        /// <param name="mp">The mean/precision pair of the distribution</param>
        /// <returns>The log of the density value</returns>
        public double DensityLn(MeanPrecisionPair mp)
        {
            return DensityLn(mp.Mean, mp.Precision);
        }

        /// <summary>
        /// Evaluates the log probability density function for a NormalGamma distribution.
        /// </summary>
        /// <param name="mean">The mean of the distribution</param>
        /// <param name="prec">The precision of the distribution</param>
        /// <returns>The log of the density value</returns>
        public double DensityLn(double mean, double prec)
        {
            if (Double.IsPositiveInfinity(_precisionInvScale) && _meanScale == 0.0)
            {
                throw new NotSupportedException();
            }

            if (Double.IsPositiveInfinity(_precisionInvScale))
            {
                throw new NotSupportedException();
            }

            if (_meanScale <= 0.0)
            {
                throw new NotSupportedException();
            }

            // double e = -0.5 * prec * (mean - _meanLocation) * (mean - _meanLocation) - prec * _precisionInvScale;
            // return (_precisionShape - 0.5) * Math.Log(prec) + _precisionShape * Math.Log(_precisionInvScale) + e - Constants.LogSqrt2Pi - SpecialFunctions.GammaLn(_precisionShape);
            double e = -(0.5*prec*_meanScale*(mean - _meanLocation)*(mean - _meanLocation)) - (prec*_precisionInvScale);
            return ((_precisionShape - 0.5)*Math.Log(prec)) + (_precisionShape*Math.Log(_precisionInvScale)) - (0.5*Math.Log(_meanScale)) + e - Constants.LogSqrt2Pi - SpecialFunctions.GammaLn(_precisionShape);
        }

        /// <summary>
        /// Generates a sample from the <c>NormalGamma</c> distribution.
        /// </summary>
        /// <returns>a sample from the distribution.</returns>
        public MeanPrecisionPair Sample()
        {
            return Sample(RandomSource, _meanLocation, _meanScale, _precisionShape, _precisionInvScale);
        }

        /// <summary>
        /// Generates a sequence of samples from the <c>NormalGamma</c> distribution
        /// </summary>
        /// <returns>a sequence of samples from the distribution.</returns>
        public IEnumerable<MeanPrecisionPair> Samples()
        {
            while (true)
            {
                yield return Sample(RandomSource, _meanLocation, _meanScale, _precisionShape, _precisionInvScale);
            }
        }

        /// <summary>
        /// Generates a sample from the <c>NormalGamma</c> distribution.
        /// </summary>
        /// <param name="rnd">The random number generator to use.</param>
        /// <param name="meanLocation">The location of the mean.</param>
        /// <param name="meanScale">The scale of the mean.</param>
        /// <param name="precisionShape">The shape of the precision.</param>
        /// <param name="precisionInverseScale">The inverse scale of the precision.</param>
        /// <returns>a sample from the distribution.</returns>
        public static MeanPrecisionPair Sample(Random rnd, double meanLocation, double meanScale, double precisionShape, double precisionInverseScale)
        {
            if (Control.CheckDistributionParameters && !IsValidParameterSet(meanLocation, meanScale, precisionShape, precisionInverseScale))
            {
                throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
            }

            var mp = new MeanPrecisionPair();

            // Sample the precision.
            mp.Precision = Double.IsPositiveInfinity(precisionInverseScale) ? precisionShape : Gamma.Sample(rnd, precisionShape, precisionInverseScale);

            // Sample the mean.
            mp.Mean = meanScale == 0.0 ? meanLocation : Normal.Sample(rnd, meanLocation, Math.Sqrt(1.0/(meanScale*mp.Precision)));

            return mp;
        }

        /// <summary>
        /// Generates a sequence of samples from the NormalGamma distribution
        /// </summary>
        /// <param name="rnd">The random number generator to use.</param>
        /// <param name="meanLocation">The location of the mean.</param>
        /// <param name="meanScale">The scale of the mean.</param>
        /// <param name="precisionShape">The shape of the precision.</param>
        /// <param name="precisionInvScale">The inverse scale of the precision.</param>
        /// <returns>a sequence of samples from the distribution.</returns>
        public static IEnumerable<MeanPrecisionPair> Samples(Random rnd, double meanLocation, double meanScale, double precisionShape, double precisionInvScale)
        {
            if (Control.CheckDistributionParameters && !IsValidParameterSet(meanLocation, meanScale, precisionShape, precisionInvScale))
            {
                throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
            }

            while (true)
            {
                var mp = new MeanPrecisionPair();

                // Sample the precision.
                mp.Precision = Double.IsPositiveInfinity(precisionInvScale) ? precisionShape : Gamma.Sample(rnd, precisionShape, precisionInvScale);

                // Sample the mean.
                mp.Mean = meanScale == 0.0 ? meanLocation : Normal.Sample(rnd, meanLocation, Math.Sqrt(1.0/(meanScale*mp.Precision)));

                yield return mp;
            }
        }
    }
}