/**
* Returns the empirical Bayes estimate of a single value.
*
* @param x the value
* @return the empirical Bayes estimate
*/
public double empiricalBayesEstimate(double x) {
if (Math.abs(x) > 10) return x; // pratical consideration; modify later
DoubleVector d = Maths.dnormLog(x, mixingDistribution.getPointValues(), 1);
d.minusEquals(d.max());
d = d.map("java.lang.Math", "exp");
d.timesEquals(mixingDistribution.getFunctionValues());
return mixingDistribution.getPointValues().innerProduct(d) / d.sum();
}
/**
* Computes the value of h(x) / f(x) given the mixture. The implementation avoided overflow.
*
* @param AHat the value
* @return the value of h(x) / f(x)
*/
public double hf(double AHat) {
DoubleVector points = mixingDistribution.getPointValues();
DoubleVector values = mixingDistribution.getFunctionValues();
double x = Math.sqrt(AHat);
DoubleVector mean = points.sqrt();
DoubleVector d1 = Maths.dnormLog(x, mean, 1);
double d1max = d1.max();
d1.minusEquals(d1max);
DoubleVector d2 = Maths.dnormLog(-x, mean, 1);
d2.minusEquals(d1max);
d1 = d1.map("java.lang.Math", "exp");
d1.timesEquals(values);
d2 = d2.map("java.lang.Math", "exp");
d2.timesEquals(values);
return ((points.minus(x / 2)).innerProduct(d1) - (points.plus(x / 2)).innerProduct(d2))
/ (d1.sum() + d2.sum());
}
/**
* Computes the value of h(x) / f(x) given the mixture. The implementation avoided overflow.
*
* @param x the value
* @return the value of h(x) / f(x)
*/
public double hf(double x) {
DoubleVector points = mixingDistribution.getPointValues();
DoubleVector values = mixingDistribution.getFunctionValues();
DoubleVector d = Maths.dnormLog(x, points, 1);
d.minusEquals(d.max());
d = (DoubleVector) d.map("java.lang.Math", "exp");
d.timesEquals(values);
return ((DoubleVector) points.times(2 * x).minusEquals(x * x)).innerProduct(d) / d.sum();
}