Ported F# MCMC samples.

src/FSharpExamples/FSharpExamples.fsproj

@@ -53,6 +53,7 @@
     <Compile Include="DenseVector.fs" />
     <Compile Include="Apply.fs" />
     <Compile Include="Histogram.fs" />
+    <Compile Include="MCMC.fs" />
   </ItemGroup>
   <Import Project="$(MSBuildExtensionsPath)\FSharp\1.0\Microsoft.FSharp.Targets" />
   <!-- To modify your build process, add your task inside one of the targets below and uncomment it. 

src/FSharpExamples/MCMC.fs

@@ -0,0 +1,201 @@
+// <copyright file="MCMC.fs" company="Math.NET">
+// Math.NET Numerics, part of the Math.NET Project
+// http://mathnet.opensourcedotnet.info
+//
+// Copyright (c) 2009 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>
+module MathNet.Numerics.FSharp.Examples.Mcmc
+
+open MathNet.Numerics.Random
+open MathNet.Numerics.Statistics
+open MathNet.Numerics.Distributions
+open MathNet.Numerics.Statistics.Mcmc
+
+/// The number of samples to gather for each sampler.
+let N = 10000
+/// The random number generator we use for the examples.
+let rnd = new MersenneTwister()
+
+//
+// Example 1: Sampling a Beta distributed variable through rejection sampling.
+//
+// Target Distribution: Beta(2.7, 6.3)
+//
+// -----------------------------------------------------------------------------
+do
+    printfn "Rejection Sampling Example"
+    
+    /// The target distribution.
+    let beta = new Beta(2.7, 6.3)
+
+    /// Samples uniform distributed variables.
+    let uniform = new ContinuousUniform(0.0, 1.0, RandomSource = rnd)
+
+    /// Implements the rejection sampling procedure.
+    let rs = new RejectionSampler<float>( ( fun x -> x**(beta.A-1.0) * (1.0 - x)**(beta.B-1.0) ),
+                                          ( fun x -> 0.021 ),
+                                          ( fun () -> uniform.Sample()) )
+
+    /// An array of samples from the rejection sampler.
+    let arr = rs.Sample(N)
+
+    /// The true distribution.
+    printfn "\tEmpirical Mean = %f (should be %f)" (Statistics.Mean(arr)) beta.Mean
+    printfn "\tEmpirical StdDev = %f (should be %f)" (Statistics.StandardDeviation(arr)) beta.StdDev
+    printfn "\tAcceptance rate = %f" rs.AcceptanceRate
+    printfn ""
+
+
+
+//
+// Example 2: Sampling a normal distributed variable through Metropolis sampling.
+//
+// Target Distribution: Normal(1.0, 3.5)
+//
+// -----------------------------------------------------------------------------
+do
+    printfn "Metropolis Sampling Example"
+    
+    let mean, stddev = 1.0, 3.5
+    let normal = new Normal(mean, stddev)
+
+    /// Implements the rejection sampling procedure.
+    let ms = new MetropolisSampler<float>( 0.1, (fun x -> log(normal.Density(x))),
+                                                (fun x -> Normal.Sample(rnd, x, 0.3)), 20,
+                                                RandomSource = rnd )
+
+    /// An array of samples from the rejection sampler.
+    let arr = ms.Sample(N)
+
+    /// The true distribution.
+    printfn "\tEmpirical Mean = %f (should be %f)" (Statistics.Mean(arr)) normal.Mean
+    printfn "\tEmpirical StdDev = %f (should be %f)" (Statistics.StandardDeviation(arr)) normal.StdDev
+    printfn "\tAcceptance rate = %f" ms.AcceptanceRate
+    printfn ""
+    
+
+
+//
+// Example 3: Sampling a normal distributed variable through Metropolis-Hastings sampling
+//              with a symmetric proposal distribution.
+//
+// Target Distribution: Normal(1.0, 3.5)
+//
+// -----------------------------------------------------------------------------------------
+do
+    printfn "Metropolis Hastings Sampling Example (Symmetric Proposal)"
+    let mean, stddev = 1.0, 3.5
+    let normal = new Normal(mean, stddev)
+    
+    /// Evaluates the log normal distribution.
+    let npdf x m s = -0.5*(x-m)*(x-m)/(s*s) - 0.5 * log(2.0 * System.Math.PI * s * s)
+
+    /// Implements the rejection sampling procedure.
+    let ms = new MetropolisHastingsSampler<float>( 0.1, (fun x -> log(normal.Density(x))), 
+                    (fun x y -> npdf x y 0.3), (fun x -> Normal.Sample(rnd, x, 0.3)), 10,
+                                                RandomSource = rnd )
+
+    /// An array of samples from the rejection sampler.
+    let arr = ms.Sample(N)
+
+    /// The true distribution.
+    printfn "\tEmpirical Mean = %f (should be %f)" (Statistics.Mean(arr)) normal.Mean
+    printfn "\tEmpirical StdDev = %f (should be %f)" (Statistics.StandardDeviation(arr)) normal.StdDev
+    printfn "\tAcceptance rate = %f" ms.AcceptanceRate
+    printfn ""
+
+
+
+//
+// Example 4: Sampling a normal distributed variable through Metropolis-Hastings sampling
+//              with a asymmetric proposal distribution.
+//
+// Target Distribution: Normal(1.0, 3.5)
+//
+// -----------------------------------------------------------------------------------------
+do
+    printfn "Metropolis Hastings Sampling Example (Assymetric Proposal)"
+    let mean, stddev = 1.0, 3.5
+    let normal = new Normal(mean, stddev)
+    
+    /// Evaluates the logarithm of the normal distribution function.
+    let npdf x m s = -0.5*(x-m)*(x-m)/(s*s) - 0.5 * log(2.0 * System.Math.PI * s * s)
+    
+    /// Samples from a mixture that is biased towards samples larger than x.
+    let mixSample x =
+        if Bernoulli.Sample(rnd, 0.5) = 1 then
+            Normal.Sample(rnd, x, 0.3)
+        else
+            Normal.Sample(rnd, x + 0.1, 0.3)
+    
+    /// The transition kernel for the proposal above.
+    let krnl xnew x = log (0.5 * exp(npdf xnew x 0.3) + 0.5 * exp(npdf xnew (x+0.1) 0.3))
+
+    /// Implements the rejection sampling procedure.
+    let ms = new MetropolisHastingsSampler<float>( 0.1, (fun x -> log(normal.Density(x))), 
+                    (fun xnew x -> krnl xnew x), (fun x -> mixSample x), 10,
+                                                RandomSource = rnd )
+
+    /// An array of samples from the rejection sampler.
+    let arr = ms.Sample(N)
+
+    /// The true distribution.
+    printfn "\tEmpirical Mean = %f (should be %f)" (Statistics.Mean(arr)) normal.Mean
+    printfn "\tEmpirical StdDev = %f (should be %f)" (Statistics.StandardDeviation(arr)) normal.StdDev
+    printfn "\tAcceptance rate = %f" ms.AcceptanceRate
+    printfn ""
+
+
+
+//
+// Example 5: Slice sampling a normal distributed random variable.
+//
+// Target Distribution: Normal(1.0, 3.5)
+//
+// -----------------------------------------------------------------------------------------
+do
+    printfn "Slice Sampling Example"
+    let mean, stddev = 1.0, 3.5
+    let normal = new Normal(mean, stddev)
+    
+    /// Evaluates the unnormalized logarithm of the normal distribution function.
+    let npdf x m s = -0.5*(x-m)*(x-m)/(s*s)
+
+    /// Implements the rejection sampling procedure.
+    let ms = new UnivariateSliceSampler( 0.1, (fun x -> npdf x mean stddev), 5, 1.0, RandomSource = rnd )
+
+    /// An array of samples from the rejection sampler.
+    let arr = ms.Sample(N)
+
+    /// The true distribution.
+    printfn "\tEmpirical Mean = %f (should be %f)" (Statistics.Mean(arr)) normal.Mean
+    printfn "\tEmpirical StdDev = %f (should be %f)" (Statistics.StandardDeviation(arr)) normal.StdDev
+    printfn ""
+
+
+
+
+
+
+System.Console.ReadLine() |> ignore