Implementation of Hybrid Monte Carlo method

src/Numerics/Numerics.csproj

@@ -411,7 +411,7 @@
     <Compile Include="Statistics\Histogram.cs" />
     <Compile Include="Statistics\MCMC\HybridMC.cs" />
     <Compile Include="Statistics\MCMC\HybridMCGeneric.cs" />
-    <Compile Include="Statistics\MCMC\MCMCDiagonistics.cs" />
+    <Compile Include="Statistics\MCMC\MCMCDiagnostics.cs" />
     <Compile Include="Statistics\MCMC\MCMCSampler.cs" />
     <Compile Include="Statistics\MCMC\MetropolisHastingsSampler.cs" />
     <Compile Include="Statistics\MCMC\MetropolisSampler.cs" />

src/Numerics/Statistics/MCMC/MCMCDiagnostics.cs

@@ -0,0 +1,91 @@
+// <copyright file="MCMCDiagonistics.cs" company="Math.NET">
+// Math.NET Numerics, part of the Math.NET Project
+// http://numerics.mathdotnet.com
+// http://github.com/mathnet/mathnet-numerics
+// http://mathnetnumerics.codeplex.com
+//
+// Copyright (c) 2009-2010 Math.NET
+//
+// Permission is hereby granted, free of charge, to any person
+// obtaining a copy of this software and associated documentation
+// files (the "Software"), to deal in the Software without
+// restriction, including without limitation the rights to use,
+// copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the
+// Software is furnished to do so, subject to the following
+// conditions:
+//
+// The above copyright notice and this permission notice shall be
+// included in all copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+// OTHER DEALINGS IN THE SOFTWARE.
+// </copyright>
+
+using System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Text;
+using System.Numerics;
+
+namespace MathNet.Numerics.Statistics.Mcmc.Diagnostics
+{
+
+
+    /// <summary>
+    /// Provides utilities to analysis the convergence of a set of samples from 
+    /// a <seealso cref="McmcSampler{T}"/>.
+    /// </summary>
+    static public class MCMCDiagnostics
+    {
+        /// <summary>
+        /// Computes the auto correlations of a series evaluated by a function f. 
+        /// </summary>
+        /// <param name="Series">The series for computing the auto correlation.</param>
+        /// <param name="lag">The lag in the series</param>
+        /// <param name="f">The function used to evaluate the series.</param>
+        /// <returns>The auto correlation.</returns>
+        /// <exception cref="ArgumentOutOfRangeException">Throws if lag is zero or if lag is 
+        /// greater than or equal to the length of Series.</exception>
+        static public double ACF<T>(IEnumerable<T> Series, int lag, Func<T,double> f)
+        {
+            if (lag < 0)
+                throw new ArgumentOutOfRangeException("Lag must be positive");
+
+            int Length = Series.Count();
+            if (lag >= Length)
+                throw new ArgumentOutOfRangeException("Lag must be smaller than the sample size");
+
+            var TransformedSeries = from data in Series
+                                select f(data);
+
+            var FirstSeries = TransformedSeries.Take(Length-lag);
+
+            var SecondSeries = TransformedSeries.Skip(lag);
+            
+            return Correlation.Pearson(FirstSeries, SecondSeries);
+
+        }
+
+        /// <summary>
+        /// Computes the effective size of the sample when evaluated by a function f.
+        /// </summary>
+        /// <param name="Series">The samples.</param>
+        /// <param name="f">The function use for evaluating the series.</param>
+        /// <returns>The effective size when auto correlation is taken into account.</returns>
+        static public double EffectiveSize<T>(IEnumerable<T> Series, Func<T,double> f)
+        {
+            int Length = Series.Count();
+            double rho = ACF(Series, 1, f);
+            return ((1 - rho) / (1 + rho)) * Length;
+
+
+        }
+    }
+}

src/UnitTests/StatisticsTests/MCMCTests/HybridMCTest.cs

@@ -37,7 +37,7 @@ using MathNet.Numerics.Random;
 using NUnit.Framework;
 using MathNet.Numerics.Statistics;
 using MathNet.Numerics.Statistics.Mcmc;
-using MathNet.Numerics.Statistics.Mcmc.Diagonistics;
+using MathNet.Numerics.Statistics.Mcmc.Diagnostics;
 
 namespace MathNet.Numerics.UnitTests.StatisticsTests.McmcTests
 {
@@ -170,7 +170,7 @@ namespace MathNet.Numerics.UnitTests.StatisticsTests.McmcTests
 
             for (int i = 0; i < 2; i++)
             {
-                Convergence[i] = 1 / Math.Sqrt(MCMCDiagonistics.EffectiveSize(Sample,x=>x[i]));
+                Convergence[i] = 1 / Math.Sqrt(MCMCDiagnostics.EffectiveSize(Sample,x=>x[i]));
                 DescriptiveStatistics Stats = new DescriptiveStatistics(NewSamples[i]);
                 SampleMean[i] = Stats.Mean;
                 SampleSdv[i] = Stats.StandardDeviation;
@@ -185,7 +185,7 @@ namespace MathNet.Numerics.UnitTests.StatisticsTests.McmcTests
                 Assert.AreEqual(SampleSdv[i] * SampleSdv[i], Sdv[i] * Sdv[i], 10 * Convergence[i], index + "Standard Deviation");
             }
 
-            double ConvergenceRho=1/Math.Sqrt(MCMCDiagonistics.EffectiveSize(Sample,x=>(x[0]-SampleMean[0])*(x[1]-SampleMean[1])));
+            double ConvergenceRho=1/Math.Sqrt(MCMCDiagnostics.EffectiveSize(Sample,x=>(x[0]-SampleMean[0])*(x[1]-SampleMean[1])));
 
             Assert.AreEqual(SampleRho*SampleSdv[0]*SampleSdv[1], rho*Sdv[0]*Sdv[1], 10 * ConvergenceRho, "Rho");
 

src/UnitTests/StatisticsTests/MCMCTests/MCMCDiagnosticsTest.cs

@@ -0,0 +1,141 @@
+// <copyright file="MCMCDiagonistics.cs" company="Math.NET">
+// Math.NET Numerics, part of the Math.NET Project
+// http://numerics.mathdotnet.com
+// http://github.com/mathnet/mathnet-numerics
+// http://mathnetnumerics.codeplex.com
+//
+// Copyright (c) 2009-2010 Math.NET
+//
+// Permission is hereby granted, free of charge, to any person
+// obtaining a copy of this software and associated documentation
+// files (the "Software"), to deal in the Software without
+// restriction, including without limitation the rights to use,
+// copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the
+// Software is furnished to do so, subject to the following
+// conditions:
+//
+// The above copyright notice and this permission notice shall be
+// included in all copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+// OTHER DEALINGS IN THE SOFTWARE.
+// </copyright>
+
+using System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Text;
+
+using NUnit.Framework;
+using MathNet.Numerics.Statistics;
+using MathNet.Numerics.Distributions;
+using MathNet.Numerics.Statistics.Mcmc.Diagnostics;
+using MathNet.Numerics.Random;
+
+namespace MathNet.Numerics.UnitTests.StatisticsTests.McmcTests
+{
+    /// <summary>
+    /// MCMCDiagonistics testing.
+    /// </summary>
+    [TestFixture]
+    public class MCMCDiagnosticsTest
+    {
+        /// <summary>
+        /// For generation of a random series to test the methods.
+        /// </summary>
+        private System.Random rnd = new System.Random();
+        /// <summary>
+        /// Distribution to sample the entries of the random series from.
+        /// </summary>
+        private Normal dis = new Normal(0, 1);
+
+
+        /// <summary>
+        /// Testing the ACF function using a randomly generated series with a range
+        /// of lags.
+        /// </summary>
+        /// <param name="startlag">Minimum value of lag in the test.</param>
+        /// <param name="endlag">Maximum value of lag in the test.</param>
+        [TestCase(0, 10)]
+        [TestCase(11, 20)]
+        [TestCase(21, 30)]
+        [TestCase(31, 40)]
+        public void TestACF(int startlag, int endlag)
+        {
+            for (int lag = startlag; lag < endlag; lag++)
+            {
+                int Length = 10000;
+                double[] firstSeries = new double[Length - lag];
+                double[] secondSeries = new double[Length - lag];
+
+                double[] Series = new double[Length];
+
+                for (int i = 0; i < Length; i++)
+                { Series[i] = RandomSeries(); }
+
+                double[] TransformedSeries = new double[Length];
+                for (int i = 0; i < Length; i++)
+                { TransformedSeries[i] = Series[i] * Series[i]; }
+
+                Array.Copy(TransformedSeries, firstSeries, Length - lag);
+                Array.Copy(TransformedSeries, lag, secondSeries, 0, Length - lag);
+
+                double result = MCMCDiagnostics.ACF(Series, lag, x=>x*x);
+                double correlation = Correlation.Pearson(firstSeries, secondSeries);
+                Assert.AreEqual(result, correlation, 10e-13);
+
+            }
+        }
+
+        /// <summary>
+        /// Set lag to be greater than the length of the series throws a 
+        /// <c>ArgumentOutOfRangeException</c>.
+        /// </summary>
+        [Test]
+        public void LagOutOfRange()
+        {
+            int Length = 10;
+            double[] Series = new double[Length];
+            Assert.Throws<ArgumentOutOfRangeException>(() => MCMCDiagnostics.ACF(Series, 11, x=>x));
+
+        }
+        /// <summary>
+        /// Set lag to be negative throws a <c>ArgumentOutOfRangeException</c>.
+        /// </summary>
+        [Test]
+        public void LagNegative()
+        {
+            Assert.Throws<ArgumentOutOfRangeException>(() => MCMCDiagnostics.ACF(new double[10], -1, x=>x));
+        }
+
+        /// <summary>
+        /// Generating a random number used for the entry of the series.
+        /// </summary>
+        /// <returns>A random number.</returns>
+        private double RandomSeries()
+        { return rnd.NextDouble() + rnd.NextDouble() * (dis.Sample()); }
+
+        /// <summary>
+        /// Testing the effective size using a random series. 
+        /// </summary>
+        [Test]
+        public void EffectiveSizeTest()
+        {
+            int Length = 10;
+            double[] Series = new double[Length];
+            for (int i = 0; i < Length; i++)
+            { Series[i] = RandomSeries(); }
+
+            double rho = MCMCDiagnostics.ACF(Series, 1,x=>x*x);
+            double ESS = (1 - rho) / (1 + rho) * Length;
+            Assert.AreEqual(ESS, MCMCDiagnostics.EffectiveSize(Series,x=>x*x), 10e-13);
+        }
+    }
+}

src/UnitTests/StatisticsTests/MCMCTests/UnivariateHybridMCTest.cs

@@ -37,7 +37,7 @@ using MathNet.Numerics.Distributions;
 using MathNet.Numerics.Random;
 using NUnit.Framework;
 using MathNet.Numerics.Statistics.Mcmc;
-using MathNet.Numerics.Statistics.Mcmc.Diagonistics;
+using MathNet.Numerics.Statistics.Mcmc.Diagnostics;
 using MathNet.Numerics.Statistics;
 
 
@@ -142,7 +142,7 @@ namespace MathNet.Numerics.UnitTests.StatisticsTests.McmcTests
 
             double[] Sample = Hybrid.Sample(10000);
 
-            double Effective = MCMCDiagonistics.EffectiveSize(Sample,x=>x);
+            double Effective = MCMCDiagnostics.EffectiveSize(Sample,x=>x);
 
             DescriptiveStatistics Stats = new DescriptiveStatistics(Sample);
 

src/UnitTests/UnitTests.csproj

@@ -754,7 +754,7 @@
     <Compile Include="StatisticsTests\DescriptiveStatisticsTests.cs" />
     <Compile Include="StatisticsTests\HistogramTests.cs" />
     <Compile Include="StatisticsTests\MCMCTests\HybridMCTest.cs" />
-    <Compile Include="StatisticsTests\MCMCTests\MCMCDiagonisticsTest.cs" />
+    <Compile Include="StatisticsTests\MCMCTests\MCMCDiagnosticsTest.cs" />
     <Compile Include="StatisticsTests\MCMCTests\MetropolisHastingsSamplerTests.cs" />
     <Compile Include="StatisticsTests\MCMCTests\MetropolisSamplerTests.cs" />
     <Compile Include="StatisticsTests\MCMCTests\RejectionSamplerTests.cs" />