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

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namespace MathNet.Numerics.Statistics.Mcmc
{
    using System;
    using Properties;

    /// <summary>
    /// Rejection sampling produces samples from distribition P by sampling from a proposal distribution Q
    /// and accepting/rejecting based on the density of P and Q. The density of P and Q don't need to
    /// to be normalized, but we do need that for each x, P(x) &lt; Q(x).
    /// </summary>
    /// <typeparam name="T">The type of samples this sampler produces.</typeparam>
    public class RejectionSampler<T> : McmcSampler<T>
    {
        /// <summary>
        /// Evaluates the density function of the sampling distribution.
        /// </summary>
        private readonly Density<T> mPdfP;

        /// <summary>
        /// Evaluates the density function of the proposal distribution.
        /// </summary>
        private readonly Density<T> mPdfQ;

        /// <summary>
        /// A function which samples from a proposal distribution.
        /// </summary>
        private readonly GlobalProposalSampler<T> mProposal;

        /// <summary>
        /// Constructs a new rejection sampler using the default <see cref="System.Random"/> random number generator.
        /// </summary>
        /// <param name="pdfP">The density of the distribution we want to sample from.</param>
        /// <param name="pdfQ">The density of the proposal distribution.</param>
        /// <param name="proposal">A method that samples from the proposal distribution.</param>
        public RejectionSampler(Density<T> pdfP, Density<T> pdfQ, GlobalProposalSampler<T> proposal)
        {
            mPdfP = pdfP;
            mPdfQ = pdfQ;
            mProposal = proposal;
        }

        /// <summary>
        /// Returns a sample from the distribution P.
        /// </summary>
        /// <exception cref="ArgumentOutOfRangeException">When the algorithms detects that the proposal
        /// distribution doesn't upper bound the target distribution.</exception>
        public override T Sample()
        {
            while (true)
            {
                // Get a sample from the proposal.
                T x = mProposal();
                // Evaluate the density for proposal.
                double q = mPdfQ(x);
                // Evaluate the density for the target density.
                double p = mPdfP(x);
                // Sample a variable between 0.0 and proposal density.
                double u = RandomSource.NextDouble() * q;

                mSamples++;

                if (q < p)
                {
                    throw new ArgumentOutOfRangeException(Resources.ProposalDistributionNoUpperBound);
                }
                if (u < p)
                {
                    mAccepts++;
                    return x;
                }
            }
        }
    }
}