// <copyright file="NormalGamma.cs" company="Math.NET">
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// Math.NET Numerics, part of the Math.NET Project
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// http://numerics.mathdotnet.com
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// http://github.com/mathnet/mathnet-numerics
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//
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// Copyright (c) 2009-2013 Math.NET
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//
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// Permission is hereby granted, free of charge, to any person
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// obtaining a copy of this software and associated documentation
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// files (the "Software"), to deal in the Software without
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// restriction, including without limitation the rights to use,
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// copy, modify, merge, publish, distribute, sublicense, and/or sell
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// copies of the Software, and to permit persons to whom the
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// Software is furnished to do so, subject to the following
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// conditions:
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//
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// The above copyright notice and this permission notice shall be
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// included in all copies or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
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// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
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// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
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// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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// OTHER DEALINGS IN THE SOFTWARE.
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// </copyright>
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using System;
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using System.Collections.Generic;
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using IStation.Numerics.Random;
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namespace IStation.Numerics.Distributions
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{
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/// <summary>
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/// This structure represents the type over which the <see cref="NormalGamma"/> distribution
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/// is defined.
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/// </summary>
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public struct MeanPrecisionPair
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{
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/// <summary>
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/// Initializes a new instance of the <see cref="MeanPrecisionPair"/> struct.
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/// </summary>
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/// <param name="m">The mean of the pair.</param>
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/// <param name="p">The precision of the pair.</param>
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public MeanPrecisionPair(double m, double p)
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{
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Mean = m;
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Precision = p;
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}
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/// <summary>
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/// Gets or sets the mean of the pair.
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/// </summary>
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public double Mean { get; set; }
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/// <summary>
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/// Gets or sets the precision of the pair.
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/// </summary>
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public double Precision { get; set; }
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}
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/// <summary>
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/// Multivariate Normal-Gamma Distribution.
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/// <para>The <see cref="NormalGamma"/> distribution is the conjugate prior distribution for the <see cref="Normal"/>
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/// distribution. It specifies a prior over the mean and precision of the <see cref="Normal"/> distribution.</para>
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/// <para>It is parameterized by four numbers: the mean location, the mean scale, the precision shape and the
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/// precision inverse scale.</para>
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/// <para>The distribution NG(mu, tau | mloc,mscale,psscale,pinvscale) = Normal(mu | mloc, 1/(mscale*tau)) * Gamma(tau | psscale,pinvscale).</para>
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/// <para>The following degenerate cases are special: when the precision is known,
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/// the precision shape will encode the value of the precision while the precision inverse scale is positive
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/// infinity. When the mean is known, the mean location will encode the value of the mean while the scale
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/// will be positive infinity. A completely degenerate NormalGamma distribution with known mean and precision is possible as well.</para>
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/// <a href="http://en.wikipedia.org/wiki/Normal-gamma_distribution">Wikipedia - Normal-Gamma distribution</a>.
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/// </summary>
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public class NormalGamma : IDistribution
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{
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System.Random _random;
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readonly double _meanLocation;
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readonly double _meanScale;
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readonly double _precisionShape;
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readonly double _precisionInvScale;
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/// <summary>
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/// Initializes a new instance of the <see cref="NormalGamma"/> class.
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/// </summary>
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/// <param name="meanLocation">The location of the mean.</param>
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/// <param name="meanScale">The scale of the mean.</param>
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/// <param name="precisionShape">The shape of the precision.</param>
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/// <param name="precisionInverseScale">The inverse scale of the precision.</param>
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public NormalGamma(double meanLocation, double meanScale, double precisionShape, double precisionInverseScale)
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{
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if (Control.CheckDistributionParameters && !IsValidParameterSet(meanLocation, meanScale, precisionShape, precisionInverseScale))
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{
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throw new ArgumentException("Invalid parametrization for the distribution.");
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}
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_random = SystemRandomSource.Default;
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_meanLocation = meanLocation;
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_meanScale = meanScale;
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_precisionShape = precisionShape;
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_precisionInvScale = precisionInverseScale;
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}
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/// <summary>
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/// Initializes a new instance of the <see cref="NormalGamma"/> class.
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/// </summary>
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/// <param name="meanLocation">The location of the mean.</param>
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/// <param name="meanScale">The scale of the mean.</param>
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/// <param name="precisionShape">The shape of the precision.</param>
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/// <param name="precisionInverseScale">The inverse scale of the precision.</param>
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/// <param name="randomSource">The random number generator which is used to draw random samples.</param>
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public NormalGamma(double meanLocation, double meanScale, double precisionShape, double precisionInverseScale, System.Random randomSource)
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{
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if (Control.CheckDistributionParameters && !IsValidParameterSet(meanLocation, meanScale, precisionShape, precisionInverseScale))
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{
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throw new ArgumentException("Invalid parametrization for the distribution.");
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}
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_random = randomSource ?? SystemRandomSource.Default;
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_meanLocation = meanLocation;
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_meanScale = meanScale;
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_precisionShape = precisionShape;
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_precisionInvScale = precisionInverseScale;
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}
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/// <summary>
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/// A string representation of the distribution.
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/// </summary>
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/// <returns>a string representation of the distribution.</returns>
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public override string ToString()
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{
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return $"NormalGamma(Mean Location = {_meanLocation}, Mean Scale = {_meanScale}, Precision Shape = {_precisionShape}, Precision Inverse Scale = {_precisionInvScale})";
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}
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/// <summary>
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/// Tests whether the provided values are valid parameters for this distribution.
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/// </summary>
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/// <param name="meanLocation">The location of the mean.</param>
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/// <param name="meanScale">The scale of the mean.</param>
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/// <param name="precShape">The shape of the precision.</param>
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/// <param name="precInvScale">The inverse scale of the precision.</param>
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public static bool IsValidParameterSet(double meanLocation, double meanScale, double precShape, double precInvScale)
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{
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return meanScale > 0.0 && precShape > 0.0 && precInvScale > 0.0 && !double.IsNaN(meanLocation);
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}
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/// <summary>
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/// Gets the location of the mean.
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/// </summary>
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public double MeanLocation => _meanLocation;
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/// <summary>
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/// Gets the scale of the mean.
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/// </summary>
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public double MeanScale => _meanScale;
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/// <summary>
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/// Gets the shape of the precision.
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/// </summary>
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public double PrecisionShape => _precisionShape;
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/// <summary>
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/// Gets the inverse scale of the precision.
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/// </summary>
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public double PrecisionInverseScale => _precisionInvScale;
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/// <summary>
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/// Gets or sets the random number generator which is used to draw random samples.
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/// </summary>
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public System.Random RandomSource
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{
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get => _random;
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set => _random = value ?? SystemRandomSource.Default;
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}
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/// <summary>
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/// Returns the marginal distribution for the mean of the <c>NormalGamma</c> distribution.
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/// </summary>
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/// <returns>the marginal distribution for the mean of the <c>NormalGamma</c> distribution.</returns>
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public StudentT MeanMarginal()
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{
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if (double.IsPositiveInfinity(_precisionInvScale))
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{
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return new StudentT(_meanLocation, 1.0/(_meanScale*_precisionShape), double.PositiveInfinity);
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}
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return new StudentT(_meanLocation, Math.Sqrt(_precisionInvScale/(_meanScale*_precisionShape)), 2.0*_precisionShape);
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}
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/// <summary>
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/// Returns the marginal distribution for the precision of the <see cref="NormalGamma"/> distribution.
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/// </summary>
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/// <returns>The marginal distribution for the precision of the <see cref="NormalGamma"/> distribution/</returns>
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public Gamma PrecisionMarginal()
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{
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return new Gamma(_precisionShape, _precisionInvScale);
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}
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/// <summary>
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/// Gets the mean of the distribution.
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/// </summary>
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/// <value>The mean of the distribution.</value>
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public MeanPrecisionPair Mean => double.IsPositiveInfinity(_precisionInvScale) ? new MeanPrecisionPair(_meanLocation, _precisionShape) : new MeanPrecisionPair(_meanLocation, _precisionShape/_precisionInvScale);
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/// <summary>
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/// Gets the variance of the distribution.
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/// </summary>
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/// <value>The mean of the distribution.</value>
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public MeanPrecisionPair Variance => new MeanPrecisionPair(_precisionInvScale/(_meanScale*(_precisionShape - 1)), _precisionShape/Math.Sqrt(_precisionInvScale));
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/// <summary>
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/// Evaluates the probability density function for a NormalGamma distribution.
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/// </summary>
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/// <param name="mp">The mean/precision pair of the distribution</param>
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/// <returns>Density value</returns>
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public double Density(MeanPrecisionPair mp)
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{
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return Density(mp.Mean, mp.Precision);
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}
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/// <summary>
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/// Evaluates the probability density function for a NormalGamma distribution.
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/// </summary>
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/// <param name="mean">The mean of the distribution</param>
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/// <param name="prec">The precision of the distribution</param>
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/// <returns>Density value</returns>
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public double Density(double mean, double prec)
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{
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if (double.IsPositiveInfinity(_precisionInvScale) && _meanScale == 0.0)
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{
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throw new NotSupportedException();
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}
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if (double.IsPositiveInfinity(_precisionInvScale))
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{
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throw new NotSupportedException();
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}
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if (_meanScale <= 0.0)
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{
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throw new NotSupportedException();
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}
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if (_precisionShape > 160.0)
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{
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return Math.Exp(DensityLn(mean, prec));
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}
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// double e = -0.5 * prec * (mean - _meanLocation) * (mean - _meanLocation) - prec * _precisionInvScale;
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// return Math.Pow(prec * _precisionInvScale, _precisionShape) * Math.Exp(e) / (Constants.Sqrt2Pi * Math.Sqrt(prec) * SpecialFunctions.Gamma(_precisionShape));
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double e = -(0.5*prec*_meanScale*(mean - _meanLocation)*(mean - _meanLocation)) - (prec*_precisionInvScale);
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return Math.Pow(prec*_precisionInvScale, _precisionShape)*Math.Exp(e)*Math.Sqrt(_meanScale)
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/(Constants.Sqrt2Pi*Math.Sqrt(prec)*SpecialFunctions.Gamma(_precisionShape));
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}
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/// <summary>
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/// Evaluates the log probability density function for a NormalGamma distribution.
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/// </summary>
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/// <param name="mp">The mean/precision pair of the distribution</param>
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/// <returns>The log of the density value</returns>
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public double DensityLn(MeanPrecisionPair mp)
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{
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return DensityLn(mp.Mean, mp.Precision);
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}
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/// <summary>
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/// Evaluates the log probability density function for a NormalGamma distribution.
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/// </summary>
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/// <param name="mean">The mean of the distribution</param>
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/// <param name="prec">The precision of the distribution</param>
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/// <returns>The log of the density value</returns>
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public double DensityLn(double mean, double prec)
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{
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if (double.IsPositiveInfinity(_precisionInvScale) && _meanScale == 0.0)
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{
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throw new NotSupportedException();
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}
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if (double.IsPositiveInfinity(_precisionInvScale))
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{
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throw new NotSupportedException();
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}
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if (_meanScale <= 0.0)
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{
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throw new NotSupportedException();
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}
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// double e = -0.5 * prec * (mean - _meanLocation) * (mean - _meanLocation) - prec * _precisionInvScale;
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// return (_precisionShape - 0.5) * Math.Log(prec) + _precisionShape * Math.Log(_precisionInvScale) + e - Constants.LogSqrt2Pi - SpecialFunctions.GammaLn(_precisionShape);
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double e = -(0.5*prec*_meanScale*(mean - _meanLocation)*(mean - _meanLocation)) - (prec*_precisionInvScale);
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return ((_precisionShape - 0.5)*Math.Log(prec)) + (_precisionShape*Math.Log(_precisionInvScale)) - (0.5*Math.Log(_meanScale)) + e - Constants.LogSqrt2Pi - SpecialFunctions.GammaLn(_precisionShape);
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}
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/// <summary>
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/// Generates a sample from the <c>NormalGamma</c> distribution.
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/// </summary>
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/// <returns>a sample from the distribution.</returns>
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public MeanPrecisionPair Sample()
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{
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return Sample(_random, _meanLocation, _meanScale, _precisionShape, _precisionInvScale);
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}
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/// <summary>
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/// Generates a sequence of samples from the <c>NormalGamma</c> distribution
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/// </summary>
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/// <returns>a sequence of samples from the distribution.</returns>
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public IEnumerable<MeanPrecisionPair> Samples()
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{
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while (true)
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{
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yield return Sample(_random, _meanLocation, _meanScale, _precisionShape, _precisionInvScale);
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}
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}
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/// <summary>
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/// Generates a sample from the <c>NormalGamma</c> distribution.
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/// </summary>
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/// <param name="rnd">The random number generator to use.</param>
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/// <param name="meanLocation">The location of the mean.</param>
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/// <param name="meanScale">The scale of the mean.</param>
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/// <param name="precisionShape">The shape of the precision.</param>
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/// <param name="precisionInverseScale">The inverse scale of the precision.</param>
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/// <returns>a sample from the distribution.</returns>
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public static MeanPrecisionPair Sample(System.Random rnd, double meanLocation, double meanScale, double precisionShape, double precisionInverseScale)
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{
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if (Control.CheckDistributionParameters && !IsValidParameterSet(meanLocation, meanScale, precisionShape, precisionInverseScale))
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{
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throw new ArgumentException("Invalid parametrization for the distribution.");
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}
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var mp = new MeanPrecisionPair();
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// Sample the precision.
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mp.Precision = double.IsPositiveInfinity(precisionInverseScale) ? precisionShape : Gamma.Sample(rnd, precisionShape, precisionInverseScale);
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// Sample the mean.
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mp.Mean = meanScale == 0.0 ? meanLocation : Normal.Sample(rnd, meanLocation, Math.Sqrt(1.0/(meanScale*mp.Precision)));
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return mp;
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}
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/// <summary>
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/// Generates a sequence of samples from the NormalGamma distribution
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/// </summary>
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/// <param name="rnd">The random number generator to use.</param>
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/// <param name="meanLocation">The location of the mean.</param>
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/// <param name="meanScale">The scale of the mean.</param>
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/// <param name="precisionShape">The shape of the precision.</param>
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/// <param name="precisionInvScale">The inverse scale of the precision.</param>
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/// <returns>a sequence of samples from the distribution.</returns>
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public static IEnumerable<MeanPrecisionPair> Samples(System.Random rnd, double meanLocation, double meanScale, double precisionShape, double precisionInvScale)
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{
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if (Control.CheckDistributionParameters && !IsValidParameterSet(meanLocation, meanScale, precisionShape, precisionInvScale))
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{
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throw new ArgumentException("Invalid parametrization for the distribution.");
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}
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while (true)
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{
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var mp = new MeanPrecisionPair();
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// Sample the precision.
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mp.Precision = double.IsPositiveInfinity(precisionInvScale) ? precisionShape : Gamma.Sample(rnd, precisionShape, precisionInvScale);
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// Sample the mean.
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mp.Mean = meanScale == 0.0 ? meanLocation : Normal.Sample(rnd, meanLocation, Math.Sqrt(1.0/(meanScale*mp.Precision)));
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yield return mp;
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}
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}
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}
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}
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