// <copyright file="MCMCDiagonistics.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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using System;
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using System.Collections.Generic;
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using System.Linq;
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namespace IStation.Numerics.Statistics.Mcmc
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{
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/// <summary>
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/// Provides utilities to analysis the convergence of a set of samples from
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/// a <seealso cref="McmcSampler{T}"/>.
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/// </summary>
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public static class MCMCDiagnostics
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{
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/// <summary>
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/// Computes the auto correlations of a series evaluated by a function f.
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/// </summary>
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/// <param name="series">The series for computing the auto correlation.</param>
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/// <param name="lag">The lag in the series</param>
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/// <param name="f">The function used to evaluate the series.</param>
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/// <returns>The auto correlation.</returns>
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/// <exception cref="ArgumentOutOfRangeException">Throws if lag is zero or if lag is
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/// greater than or equal to the length of Series.</exception>
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public static double ACF<T>(IEnumerable<T> series, int lag, Func<T,double> f)
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{
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if (lag < 0)
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{
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throw new ArgumentOutOfRangeException(nameof(lag), "Lag must be positive");
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}
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int length = series.Count();
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if (lag >= length)
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{
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throw new ArgumentOutOfRangeException(nameof(lag), "Lag must be smaller than the sample size");
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}
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var transformedSeries = series.Select(f);
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var enumerable = transformedSeries as double[] ?? transformedSeries.ToArray();
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var firstSeries = enumerable.Take(length-lag);
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var secondSeries = enumerable.Skip(lag);
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return Correlation.Pearson(firstSeries, secondSeries);
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}
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/// <summary>
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/// Computes the effective size of the sample when evaluated by a function f.
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/// </summary>
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/// <param name="series">The samples.</param>
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/// <param name="f">The function use for evaluating the series.</param>
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/// <returns>The effective size when auto correlation is taken into account.</returns>
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public static double EffectiveSize<T>(IEnumerable<T> series, Func<T,double> f)
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{
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int length = series.Count();
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double rho = ACF(series, 1, f);
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return ((1 - rho) / (1 + rho)) * length;
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}
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}
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}
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