public void LagOutOfRange()
{
const int length = 10;
var series = new double[length];
Assert.That(() => MCMCDiagnostics.ACF(series, 11, x => x), Throws.TypeOf <ArgumentOutOfRangeException>());
}
public void SampleTest(double mean, double sdv, int seed)
{
var dis = new Normal(mean, sdv);
var hybrid = new UnivariateHybridMC(0, dis.DensityLn, 10, 0.1, 1000, 1, new System.Random(seed))
{
BurnInterval = 0
};
double[] sample = hybrid.Sample(10000);
double effective = MCMCDiagnostics.EffectiveSize(sample, x => x);
var stats = new DescriptiveStatistics(sample);
//Testing the mean using the normal distribution.
double meanConvergence = 3 * sdv / Math.Sqrt(effective);
Assert.AreEqual(stats.Mean, mean, meanConvergence, "Mean");
double deviationRation = Math.Pow(stats.StandardDeviation / sdv, 2);
//Approximating chi-square with normal distribution. (Degree of freedom is large)
double deviationConvergence = 3 * Math.Sqrt(2) / Math.Sqrt(effective);
Assert.AreEqual(deviationRation, 1, deviationConvergence, "Standard Deivation");
}
public void TestACF(int startlag, int endlag)
{
for (int lag = startlag; lag < endlag; lag++)
{
const int length = 10000;
var firstSeries = new double[length - lag];
var secondSeries = new double[length - lag];
var series = new double[length];
for (int i = 0; i < length; i++)
{
series[i] = RandomSeries();
}
var 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);
}
}
public void SampleTest()
{
double Mean = 5 * rnd.NextDouble();
double Sdv = 5 * rnd.NextDouble();
Normal dis = new Normal(Mean, Sdv);
UnivariateHybridMC Hybrid = new UnivariateHybridMC(0, dis.DensityLn, 10, 0.1, 1000);
Hybrid.BurnInterval = 0;
double[] Sample = Hybrid.Sample(10000);
double Effective = MCMCDiagnostics.EffectiveSize(Sample, x => x);
DescriptiveStatistics Stats = new DescriptiveStatistics(Sample);
//Testing the mean using the normal distribution.
double MeanConvergence = 3 * Sdv / Math.Sqrt(Effective);
Assert.AreEqual(Stats.Mean, Mean, MeanConvergence, "Mean");
double DeviationRation = Math.Pow(Stats.StandardDeviation / Sdv, 2);
//Approximating chi-square with normal distribution. (Degree of freedom is large)
double DeviationConvergence = 3 * Math.Sqrt(2) / Math.Sqrt(Effective);
Assert.AreEqual(DeviationRation, 1, DeviationConvergence, "Standard Deivation");
}
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);
}
}
public void LagOutOfRange()
{
int Length = 10;
double[] Series = new double[Length];
Assert.Throws <ArgumentOutOfRangeException>(() => MCMCDiagnostics.ACF(Series, 11, x => x));
}
public void SampleTest()
{
//Variances and Means
double[] Sdv = new double[2];
double[] Mean = new double[2];
for (int i = 0; i < 2; i++)
{
Sdv[i] = RandomVar();
Mean[i] = 5 * rnd.NextDouble();
}
//Cross Variance
double rho = 1.0 - RandomVar();
DensityLn <double[]> pdfLn = new DensityLn <double[]>(x => LogDen(x, Sdv, Mean, rho));
HybridMC Hybrid = new HybridMC(new double[2] {
0, 0
}, pdfLn, 10, 0.1, 1000);
Hybrid.BurnInterval = 0;
int SampleSize = 10000;
double[][] Sample = Hybrid.Sample(SampleSize);
double[][] NewSamples = ArrangeSamples(SampleSize, Sample);
double[] Convergence = new double[2];
double[] SampleMean = new double[2];
double[] SampleSdv = new double[2];
for (int i = 0; i < 2; 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;
}
double SampleRho = Correlation.Pearson(NewSamples[0], NewSamples[1]);
for (int i = 0; i < 2; i++)
{
string index = i.ToString();
Assert.AreEqual(Mean[i], SampleMean[i], 10 * Convergence[i], index + "Mean");
Assert.AreEqual(SampleSdv[i] * SampleSdv[i], Sdv[i] * Sdv[i], 10 * Convergence[i], index + "Standard Deviation");
}
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");
}
public void EffectiveSizeTest()
{
const int length = 10;
var 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);
}
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);
}
public void SampleTest(double[] sdv, double[] mean, double rho, int seed)
{
var pdfLn = new DensityLn <double[]>(x => LogDen(x, sdv, mean, rho));
var hybrid = new HybridMC(new double[2] {
0, 0
}, pdfLn, 10, 0.1, 1000, new double[] { 1, 1 }, new System.Random(seed))
{
BurnInterval = 0
};
const int sampleSize = 10000;
double[][] sample = hybrid.Sample(sampleSize);
double[][] newSamples = ArrangeSamples(sampleSize, sample);
var convergence = new double[2];
var sampleMean = new double[2];
var sampleSdv = new double[2];
for (int i = 0; i < 2; i++)
{
convergence[i] = 1 / Math.Sqrt(MCMCDiagnostics.EffectiveSize(sample, x => x[i]));
var stats = new DescriptiveStatistics(newSamples[i]);
sampleMean[i] = stats.Mean;
sampleSdv[i] = stats.StandardDeviation;
}
double sampleRho = Correlation.Pearson(newSamples[0], newSamples[1]);
for (int i = 0; i < 2; i++)
{
string index = i.ToString();
Assert.AreEqual(mean[i], sampleMean[i], 10 * convergence[i], index + "Mean");
Assert.AreEqual(sampleSdv[i] * sampleSdv[i], sdv[i] * sdv[i], 10 * convergence[i], index + "Standard Deviation");
}
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");
}
public void LagNegative()
{
Assert.That(() => MCMCDiagnostics.ACF(new double[10], -1, x => x), Throws.TypeOf <ArgumentOutOfRangeException>());
}
private static double CalculateAutocorrelation(Signal signal, int lag)
{
return(MCMCDiagnostics.ACF(signal.Readouts, lag, x => x));
}
