public static void GetIntegrationBounds(Gamma exp, Gaussian d, out double dmode, out double dmin, out double dmax)
{
dmode = FindMaximum(exp, d);
double aMinus1 = exp.Shape - 1;
double b = exp.Rate;
double mode = dmode;
double expMode = Math.Exp(dmode);
double mode2 = dmode * dmode;
Func <double, double> func = delegate(double x)
{
if (double.IsInfinity(x))
{
return(double.NegativeInfinity);
}
double xMinusMode = x - mode;
double f = aMinus1 * xMinusMode - b * (Math.Exp(x) - expMode) + xMinusMode * d.MeanTimesPrecision + 50;
// avoid infinity*0
if (d.Precision != 0)
{
f -= 0.5 * (x * x - mode2) * d.Precision;
}
return(f);
};
Func <double, double> deriv = delegate(double x)
{
return(aMinus1 - b * Math.Exp(x) - x * d.Precision + d.MeanTimesPrecision);
};
List <double> zeroes = GaussianOp_Slow.FindZeroes(func, deriv, new double[] { dmode }, new double[0]);
dmin = MMath.Min(zeroes);
dmax = MMath.Max(zeroes);
}
public void QuantileTest()
{
// draw many samples from N(m,v)
Rand.Restart(0);
int n = 10000;
double m = 2;
double stddev = 3;
Gaussian prior = new Gaussian(m, stddev * stddev);
List <double> x = new List <double>();
for (int i = 0; i < n; i++)
{
x.Add(prior.Sample());
}
x.Sort();
var sortedData = new OuterQuantiles(x.ToArray());
// compute quantiles
var quantiles = InnerQuantiles.FromDistribution(100, sortedData);
// loop over x's and compare true quantile rank
var testPoints = EpTests.linspace(MMath.Min(x) - stddev, MMath.Max(x) + stddev, 100);
double maxError = 0;
foreach (var testPoint in testPoints)
{
var trueRank = MMath.NormalCdf((testPoint - m) / stddev);
var estRank = quantiles.GetProbLessThan(testPoint);
var error = System.Math.Abs(trueRank - estRank);
//Trace.WriteLine($"{testPoint} trueRank={trueRank} estRank={estRank} error={error}");
Assert.True(error < 0.02);
maxError = System.Math.Max(maxError, error);
double estQuantile = quantiles.GetQuantile(estRank);
error = MMath.AbsDiff(estQuantile, testPoint, 1e-8);
//Trace.WriteLine($"{testPoint} estRank={estRank} estQuantile={estQuantile} error={error}");
Assert.True(error < 1e-8);
estRank = sortedData.GetProbLessThan(testPoint);
error = System.Math.Abs(trueRank - estRank);
//Trace.WriteLine($"{testPoint} trueRank={trueRank} estRank={estRank} error={error}");
Assert.True(error < 0.02);
}
//Trace.WriteLine($"max rank error = {maxError}");
}
private void CheckProbLessThan(CanGetProbLessThan canGetProbLessThan, List <double> x, double maximumError)
{
x.Sort();
var sortedData = new OuterQuantiles(x.ToArray());
// check that quantiles match within the desired accuracy
var min = MMath.Min(x);
var max = MMath.Max(x);
var range = max - min;
var margin = range * 0.01;
var testPoints = EpTests.linspace(min - margin, max + margin, 100);
double maxError = 0;
foreach (var testPoint in testPoints)
{
var trueRank = sortedData.GetProbLessThan(testPoint);
var estRank = canGetProbLessThan.GetProbLessThan(testPoint);
var error = System.Math.Abs(trueRank - estRank);
maxError = System.Math.Max(maxError, error);
}
Console.WriteLine($"max rank error = {maxError}");
Assert.True(maxError <= maximumError);
}