mathnet-numerics/src/Numerics/Statistics/MCMC/UnivariateHybridMC.cs

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using System;
using MathNet.Numerics.Distributions;
using MathNet.Numerics.Random;

namespace MathNet.Numerics.Statistics.Mcmc
{
    /// <summary>
    /// A hybrid Monte Carlo sampler for univariate distributions.
    /// </summary>
    public class UnivariateHybridMC : HybridMCGeneric<double>
    {
        /// <summary>
        /// Distribution to sample momentum from.
        /// </summary>
        private readonly Normal _distribution;

        /// <summary>
        /// Standard deviations used in the sampling of the
        /// momentum.
        /// </summary>
        private double _sdv;

        /// <summary>
        /// Gets or sets the standard deviation used in the sampling of the
        /// momentum.
        /// </summary>
        /// <exception cref="ArgumentOutOfRangeException">When standard deviation is negative.</exception>
        public double MomentumStdDev
        {
            get { return _sdv; }
            set
            {
                if (_sdv != value)
                {
                    _sdv = SetPositive(value);
                }
            }
        }

        /// <summary>
        /// Constructs a new Hybrid Monte Carlo sampler for a univariate probability distribution.
        /// The momentum will be sampled from a normal distribution with standard deviation
        /// specified by pSdv using the default <see cref="System.Random"/> random
        /// number generator. A three point estimation will be used for differentiation.
        /// This constructor will set the burn interval.
        /// </summary>
        /// <param name="x0">The initial sample.</param>
        /// <param name="pdfLnP">The log density of the distribution we want to sample from.</param>
        /// <param name="frogLeapSteps">Number frogleap simulation steps.</param>
        /// <param name="stepSize">Size of the frogleap simulation steps.</param>
        /// <param name="burnInterval">The number of iterations in between returning samples.</param>
        /// <param name="pSdv">The standard deviation of the normal distribution that is used to sample
        /// the momentum.</param>
        /// <exception cref="ArgumentOutOfRangeException">When the number of burnInterval iteration is negative.</exception>
        public UnivariateHybridMC(double x0, DensityLn<double> pdfLnP, int frogLeapSteps, double stepSize, int burnInterval = 0, double pSdv = 1)
            : this(x0, pdfLnP, frogLeapSteps, stepSize, burnInterval, pSdv, SystemRandomSource.Default)
        {
        }

        /// <summary>
        /// Constructs a new Hybrid Monte Carlo sampler for a univariate probability distribution.
        /// The momentum will be sampled from a normal distribution with standard deviation
        /// specified by pSdv using a random
        /// number generator provided by the user. A three point estimation will be used for differentiation.
        /// This constructor will set the burn interval.
        /// </summary>
        /// <param name="x0">The initial sample.</param>
        /// <param name="pdfLnP">The log density of the distribution we want to sample from.</param>
        /// <param name="frogLeapSteps">Number frogleap simulation steps.</param>
        /// <param name="stepSize">Size of the frogleap simulation steps.</param>
        /// <param name="burnInterval">The number of iterations in between returning samples.</param>
        /// <param name="pSdv">The standard deviation of the normal distribution that is used to sample
        /// the momentum.</param>
        /// <param name="randomSource">Random number generator used to sample the momentum.</param>
        /// <exception cref="ArgumentOutOfRangeException">When the number of burnInterval iteration is negative.</exception>
        public UnivariateHybridMC(double x0, DensityLn<double> pdfLnP, int frogLeapSteps, double stepSize, int burnInterval, double pSdv, System.Random randomSource)
            : this(x0, pdfLnP, frogLeapSteps, stepSize, burnInterval, pSdv, randomSource, Grad)
        {
        }

        /// <summary>
        /// Constructs a new Hybrid Monte Carlo sampler for a multivariate probability distribution.
        /// The momentum will be sampled from a normal distribution with standard deviation
        /// given by pSdv using a random
        /// number generator provided by the user.  This constructor will set both the burn interval and the method used for
        /// numerical differentiation.
        /// </summary>
        /// <param name="x0">The initial sample.</param>
        /// <param name="pdfLnP">The log density of the distribution we want to sample from.</param>
        /// <param name="frogLeapSteps">Number frogleap simulation steps.</param>
        /// <param name="stepSize">Size of the frogleap simulation steps.</param>
        /// <param name="burnInterval">The number of iterations in between returning samples.</param>
        /// <param name="pSdv">The standard deviation of the normal distribution that is used to sample
        /// the momentum.</param>
        /// <param name="diff">The method used for numerical differentiation.</param>
        /// <param name="randomSource">Random number generator used for sampling the momentum.</param>
        /// <exception cref="ArgumentOutOfRangeException">When the number of burnInterval iteration is negative.</exception>
        public UnivariateHybridMC(double x0, DensityLn<double> pdfLnP, int frogLeapSteps, double stepSize, int burnInterval, double pSdv, System.Random randomSource, DiffMethod diff)
            : base(x0, pdfLnP, frogLeapSteps, stepSize, burnInterval, randomSource, diff)
        {
            MomentumStdDev = pSdv;
            _distribution = new Normal(0.0, MomentumStdDev, RandomSource);
            Burn(BurnInterval);
        }

        /// <summary>
        /// Use for copying objects in the Burn method.
        /// </summary>
        /// <param name="source">The source of copying.</param>
        /// <returns>A copy of the source object.</returns>
        protected override double Copy(double source)
        {
            return source;
        }

        /// <summary>
        /// Use for creating temporary objects in the Burn method.
        /// </summary>
        /// <returns>An object of type T.</returns>
        protected override double Create()
        {
            return 0;
        }

        /// <inheritdoc/>
        protected override void DoAdd(ref double first, double factor, double second)
        {
            first += factor * second;
        }

        /// <inheritdoc/>
        protected override double DoProduct(double first, double second)
        {
            return first * second;
        }

        /// <inheritdoc/>
        protected override void DoSubtract(ref double first, double factor, double second)
        {
            first -= factor * second;
        }

        /// <summary>
        /// Samples the momentum from a normal distribution.
        /// </summary>
        /// <param name="p">The momentum to be randomized.</param>
        protected override void RandomizeMomentum(ref double p)
        {
            p = _distribution.Sample();
        }

        /// <summary>
        /// The default method used for computing the derivative. Uses a simple three point estimation.
        /// </summary>
        /// <param name="function">Function for which the derivative is to be evaluated.</param>
        /// <param name="x">The location where the derivative is to be evaluated.</param>
        /// <returns>The derivative of the function at the point x.</returns>
        static double Grad(DensityLn<double> function, double x)
        {
            double h = Math.Max(10e-4, (10e-7) * x);
            double increment = x + h;
            double decrement = x - h;
            return (function(increment) - function(decrement)) / (2 * h);
        }
    }
}