// <copyright file="RejectionSampler.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) 2009-2010 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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// OTHER DEALINGS IN THE SOFTWARE.
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// </copyright>
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namespace IStation.Numerics.Statistics.Mcmc
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{
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using System;
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/// <summary>
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/// Rejection sampling produces samples from distribution P by sampling from a proposal distribution Q
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/// and accepting/rejecting based on the density of P and Q. The density of P and Q don't need to
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/// to be normalized, but we do need that for each x, P(x) < Q(x).
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/// </summary>
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/// <typeparam name="T">The type of samples this sampler produces.</typeparam>
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public class RejectionSampler<T> : McmcSampler<T>
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{
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/// <summary>
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/// Evaluates the density function of the sampling distribution.
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/// </summary>
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private readonly Density<T> _pdfP;
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/// <summary>
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/// Evaluates the density function of the proposal distribution.
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/// </summary>
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private readonly Density<T> _pdfQ;
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/// <summary>
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/// A function which samples from a proposal distribution.
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/// </summary>
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private readonly GlobalProposalSampler<T> _proposal;
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/// <summary>
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/// Constructs a new rejection sampler using the default <see cref="System.Random"/> random number generator.
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/// </summary>
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/// <param name="pdfP">The density of the distribution we want to sample from.</param>
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/// <param name="pdfQ">The density of the proposal distribution.</param>
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/// <param name="proposal">A method that samples from the proposal distribution.</param>
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public RejectionSampler(Density<T> pdfP, Density<T> pdfQ, GlobalProposalSampler<T> proposal)
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{
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_pdfP = pdfP;
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_pdfQ = pdfQ;
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_proposal = proposal;
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}
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/// <summary>
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/// Returns a sample from the distribution P.
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/// </summary>
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/// <exception cref="ArgumentOutOfRangeException">When the algorithms detects that the proposal
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/// distribution doesn't upper bound the target distribution.</exception>
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public override T Sample()
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{
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while (true)
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{
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// Get a sample from the proposal.
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T x = _proposal();
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// Evaluate the density for proposal.
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double q = _pdfQ(x);
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// Evaluate the density for the target density.
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double p = _pdfP(x);
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// Sample a variable between 0.0 and proposal density.
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double u = RandomSource.NextDouble() * q;
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Samples++;
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if (q < p)
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{
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throw new ArgumentException("The sampler\'s proposal distribution is not upper bounding the target density.");
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}
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if (u < p)
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{
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Accepts++;
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return x;
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}
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}
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}
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}
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}
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