/// <summary>
/// A-R example
/// S Chib and E Greenberg, Understanding the Metropolis-Hastings Algorithm, The American Statistician, Vol. 49, No. 4. (Nov., 1995), pp. 327-335
/// samples are tesitfied by SigmaPlot
/// </summary>
public static void Example()
{
int N = 6000;
int n0 = 0;
string filename1 = "v1.txt";
FileStream fs1 = new FileStream(filename1, FileMode.Create, FileAccess.Write);
StreamWriter w1 = new StreamWriter(fs1);
// target distribution
//double[,] S = {{1, 0.9},{0.9, 1}};
double[,] S = { { 2, 0 }, { 0, 1 } };
double[] m = { 1, 2 };
PZMath_matrix targetSigma = new PZMath_matrix(S);
PZMath_vector targetMu = new PZMath_vector(m);
// instrumental distribution
double[,] D = {{2, 0},{0, 1}};
PZMath_matrix instrumentalSigma = new PZMath_matrix(D);
PZMath_vector instrumentalMu = new PZMath_vector(m);
double c = System.Math.Sqrt(System.Math.Abs(instrumentalSigma.LUDet()) / System.Math.Abs(targetSigma.LUDet()));
// prepare workspace
AcceptRejectionSampler ARSample = new AcceptRejectionSampler(c, N);
// prepare instrumental distribution
InstrumentalDistribution instrumentalDistribution = new InstrumentalDistribution(instrumentalMu, instrumentalSigma);
// prepare target distribution
TargetDistribution targetDistribution = new TargetDistribution();
targetDistribution.TargetDistributionFunction = new targetDistribution(AcceptRejectionSampler.ExampleTargetDistributionFunction);
// assign target distribution and instrumental distribution to the work space
ARSample.ARSInstrumentalDistribution = instrumentalDistribution;
ARSample.ARSTargetDistribution = targetDistribution;
// A-R sample
List<double[]> samples = ARSample.Sample();
for (int i = 0; i < N - n0; i++)
{
w1.Write(samples[i][0]);
w1.Write(" ");
w1.WriteLine(samples[i][1]);
}
w1.Close();
fs1.Close();
}
/// <summary>
/// M-H example
/// S Chib and E Greenberg, Understanding the Metropolis-Hastings Algorithm, The American Statistician, Vol. 49, No. 4. (Nov., 1995), pp. 327-335
/// 1. random walk - uniform
/// 2. random walk - normal
/// 3. 1st order autogressive - uniform (change MH.Sample() samle method)
/// samples are tesitfied by SigmaPlot
/// </summary>
public static void Example()
{
int N = 10000;
int n0 = 1000;
// file IO
string filename1 = "v1.txt";
FileStream fs1 = new FileStream(filename1, FileMode.Create, FileAccess.Write);
StreamWriter w1 = new StreamWriter(fs1);
// target distribution
double lamda = 20;
//double r = 0.3;
double width = 1.0;
double height = 1.0;
//double theta1 = 2;
//double theta2 = -1.0;
// prepare workspace
GeyerMollerSampler GMSampler = new GeyerMollerSampler(N, n0, lamda, width, height);
// prepare target distribution
TargetDistribution targetDistribution = new TargetDistribution();
targetDistribution.TargetPointProcessDistributionFunction = new targetPointProcessDistribution(GeyerMollerSampler.ExampleTargetDistributionFunction);
// assign target distribution and instrumental distribution to the work space
GMSampler.GMTargetDistribution = targetDistribution;
// M-H sample
GMSampler.Init();
List<List<PZPoint>> samples = GMSampler.Sample();
// output samples
int sampleLength = samples.Count;
for (int i = 0; i < sampleLength; i++)
{
int xLength = samples[i].Count;
for (int j = 0; j < xLength; j++)
{
w1.Write(String.Format("{0:f}",samples[i][j].x) + " " + String.Format("{0:f}",samples[i][j].y) + " | ");
}
w1.WriteLine();
}
w1.Close();
fs1.Close();
}
/// <summary>
/// M-H example
/// S Chib and E Greenberg, Understanding the Metropolis-Hastings Algorithm, The American Statistician, Vol. 49, No. 4. (Nov., 1995), pp. 327-335
/// 1. random walk - uniform
/// 2. random walk - normal
/// 3. 1st order autogressive - uniform (change MH.Sample() samle method)
/// samples are tesitfied by SigmaPlot
/// </summary>
public static void Example()
{
int N = 10000;
int n0 = 1000;
string filename1 = "v1.txt";
FileStream fs1 = new FileStream(filename1, FileMode.Create, FileAccess.Write);
StreamWriter w1 = new StreamWriter(fs1);
// target distribution
//double[,] S = {{1, 0.9},{0.9, 1}};
double[,] S = { { 2, 0 }, { 0, 1 } };
double[] m = { 1, 2 };
PZMath_matrix targetSigma = new PZMath_matrix(S);
PZMath_vector targetMu = new PZMath_vector(m);
// candidate generating distribution
// normal
double[,] D = {{2.5, 0},{0, 1.5}};
double[] mm = { 0, 0 };
PZMath_matrix cgdSigma = new PZMath_matrix(D);
PZMath_vector cgdMu = new PZMath_vector(mm);
// uniform
double[] d = { 0.75, 1 }; // for random walk
//double[] d = { 1, 1 }; // for 1st order autogressive
// prepare workspace
MetropolisHastingsSampler MHSample = new MetropolisHastingsSampler(N, n0);
// prepare instrumental distribution
// multivariate normal candidate generating distribution
//CandidateGeneratingDistribution cgDistribution = new CandidateGeneratingDistribution(cgdMu, cgdSigma);
// multivariate-t candidate generating distribution
CandidateGeneratingDistribution cgDistribution = new CandidateGeneratingDistribution(d);
// prepare target distribution
TargetDistribution targetDistribution = new TargetDistribution();
targetDistribution.TargetDistributionFunction = new targetDistribution(MetropolisHastingsSampler.ExampleTargetDistributionFunction);
// assign target distribution and instrumental distribution to the work space
MHSample.MHCandidateGeneratingDistribution = cgDistribution;
MHSample.MHTargetDistribution = targetDistribution;
// M-H sample
double[] initX = { 1, 2 };
MHSample.Init(initX);
List<double[]> samples = MHSample.Sample();
for (int i = 0; i < N - n0; i++)
{
w1.Write(samples[i][0]);
w1.Write(" ");
w1.WriteLine(samples[i][1]);
}
w1.Close();
fs1.Close();
}
