forked from tsai/mathnet-numerics
Jurgen Van Gael
17 years ago
2 changed files with 202 additions and 0 deletions
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// <copyright file="MCMC.fs" company="Math.NET"> |
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// Math.NET Numerics, part of the Math.NET Project |
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// http://mathnet.opensourcedotnet.info |
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// |
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// Copyright (c) 2009 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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// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, |
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// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING |
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR |
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// OTHER DEALINGS IN THE SOFTWARE. |
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// </copyright> |
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module MathNet.Numerics.FSharp.Examples.Mcmc |
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open MathNet.Numerics.Random |
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open MathNet.Numerics.Statistics |
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open MathNet.Numerics.Distributions |
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open MathNet.Numerics.Statistics.Mcmc |
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/// The number of samples to gather for each sampler. |
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let N = 10000 |
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/// The random number generator we use for the examples. |
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let rnd = new MersenneTwister() |
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// |
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// Example 1: Sampling a Beta distributed variable through rejection sampling. |
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// |
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// Target Distribution: Beta(2.7, 6.3) |
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// |
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// ----------------------------------------------------------------------------- |
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do |
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printfn "Rejection Sampling Example" |
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/// The target distribution. |
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let beta = new Beta(2.7, 6.3) |
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/// Samples uniform distributed variables. |
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let uniform = new ContinuousUniform(0.0, 1.0, RandomSource = rnd) |
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/// Implements the rejection sampling procedure. |
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let rs = new RejectionSampler<float>( ( fun x -> x**(beta.A-1.0) * (1.0 - x)**(beta.B-1.0) ), |
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( fun x -> 0.021 ), |
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( fun () -> uniform.Sample()) ) |
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/// An array of samples from the rejection sampler. |
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let arr = rs.Sample(N) |
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/// The true distribution. |
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printfn "\tEmpirical Mean = %f (should be %f)" (Statistics.Mean(arr)) beta.Mean |
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printfn "\tEmpirical StdDev = %f (should be %f)" (Statistics.StandardDeviation(arr)) beta.StdDev |
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printfn "\tAcceptance rate = %f" rs.AcceptanceRate |
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printfn "" |
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// |
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// Example 2: Sampling a normal distributed variable through Metropolis sampling. |
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// |
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// Target Distribution: Normal(1.0, 3.5) |
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// |
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// ----------------------------------------------------------------------------- |
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do |
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printfn "Metropolis Sampling Example" |
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let mean, stddev = 1.0, 3.5 |
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let normal = new Normal(mean, stddev) |
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/// Implements the rejection sampling procedure. |
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let ms = new MetropolisSampler<float>( 0.1, (fun x -> log(normal.Density(x))), |
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(fun x -> Normal.Sample(rnd, x, 0.3)), 20, |
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RandomSource = rnd ) |
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/// An array of samples from the rejection sampler. |
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let arr = ms.Sample(N) |
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/// The true distribution. |
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printfn "\tEmpirical Mean = %f (should be %f)" (Statistics.Mean(arr)) normal.Mean |
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printfn "\tEmpirical StdDev = %f (should be %f)" (Statistics.StandardDeviation(arr)) normal.StdDev |
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printfn "\tAcceptance rate = %f" ms.AcceptanceRate |
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printfn "" |
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// |
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// Example 3: Sampling a normal distributed variable through Metropolis-Hastings sampling |
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// with a symmetric proposal distribution. |
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// |
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// Target Distribution: Normal(1.0, 3.5) |
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// |
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// ----------------------------------------------------------------------------------------- |
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do |
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printfn "Metropolis Hastings Sampling Example (Symmetric Proposal)" |
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let mean, stddev = 1.0, 3.5 |
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let normal = new Normal(mean, stddev) |
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/// Evaluates the log normal distribution. |
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let npdf x m s = -0.5*(x-m)*(x-m)/(s*s) - 0.5 * log(2.0 * System.Math.PI * s * s) |
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/// Implements the rejection sampling procedure. |
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let ms = new MetropolisHastingsSampler<float>( 0.1, (fun x -> log(normal.Density(x))), |
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(fun x y -> npdf x y 0.3), (fun x -> Normal.Sample(rnd, x, 0.3)), 10, |
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RandomSource = rnd ) |
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/// An array of samples from the rejection sampler. |
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let arr = ms.Sample(N) |
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/// The true distribution. |
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printfn "\tEmpirical Mean = %f (should be %f)" (Statistics.Mean(arr)) normal.Mean |
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printfn "\tEmpirical StdDev = %f (should be %f)" (Statistics.StandardDeviation(arr)) normal.StdDev |
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printfn "\tAcceptance rate = %f" ms.AcceptanceRate |
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printfn "" |
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// |
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// Example 4: Sampling a normal distributed variable through Metropolis-Hastings sampling |
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// with a asymmetric proposal distribution. |
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// |
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// Target Distribution: Normal(1.0, 3.5) |
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// |
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// ----------------------------------------------------------------------------------------- |
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do |
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printfn "Metropolis Hastings Sampling Example (Assymetric Proposal)" |
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let mean, stddev = 1.0, 3.5 |
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let normal = new Normal(mean, stddev) |
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/// Evaluates the logarithm of the normal distribution function. |
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let npdf x m s = -0.5*(x-m)*(x-m)/(s*s) - 0.5 * log(2.0 * System.Math.PI * s * s) |
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/// Samples from a mixture that is biased towards samples larger than x. |
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let mixSample x = |
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if Bernoulli.Sample(rnd, 0.5) = 1 then |
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Normal.Sample(rnd, x, 0.3) |
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else |
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Normal.Sample(rnd, x + 0.1, 0.3) |
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/// The transition kernel for the proposal above. |
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let krnl xnew x = log (0.5 * exp(npdf xnew x 0.3) + 0.5 * exp(npdf xnew (x+0.1) 0.3)) |
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/// Implements the rejection sampling procedure. |
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let ms = new MetropolisHastingsSampler<float>( 0.1, (fun x -> log(normal.Density(x))), |
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(fun xnew x -> krnl xnew x), (fun x -> mixSample x), 10, |
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RandomSource = rnd ) |
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/// An array of samples from the rejection sampler. |
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let arr = ms.Sample(N) |
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/// The true distribution. |
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printfn "\tEmpirical Mean = %f (should be %f)" (Statistics.Mean(arr)) normal.Mean |
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printfn "\tEmpirical StdDev = %f (should be %f)" (Statistics.StandardDeviation(arr)) normal.StdDev |
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printfn "\tAcceptance rate = %f" ms.AcceptanceRate |
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printfn "" |
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// |
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// Example 5: Slice sampling a normal distributed random variable. |
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// |
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// Target Distribution: Normal(1.0, 3.5) |
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// |
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// ----------------------------------------------------------------------------------------- |
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do |
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printfn "Slice Sampling Example" |
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let mean, stddev = 1.0, 3.5 |
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let normal = new Normal(mean, stddev) |
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/// Evaluates the unnormalized logarithm of the normal distribution function. |
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let npdf x m s = -0.5*(x-m)*(x-m)/(s*s) |
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/// Implements the rejection sampling procedure. |
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let ms = new UnivariateSliceSampler( 0.1, (fun x -> npdf x mean stddev), 5, 1.0, RandomSource = rnd ) |
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/// An array of samples from the rejection sampler. |
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let arr = ms.Sample(N) |
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/// The true distribution. |
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printfn "\tEmpirical Mean = %f (should be %f)" (Statistics.Mean(arr)) normal.Mean |
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printfn "\tEmpirical StdDev = %f (should be %f)" (Statistics.StandardDeviation(arr)) normal.StdDev |
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printfn "" |
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System.Console.ReadLine() |> ignore |
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