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Bayes-Laplace Rule

Name​

UxHwDoubleBayesLaplace, UxHwFloatBayesLaplace — Apply Bayes-Laplace rule to distributions.

Synopsis​

#include <uxhw.h>

double  UxHwDoubleBayesLaplace(double (*likelihood)(double), double prior, double evidence);
float   UxHwFloatBayesLaplace(float (*likelihood)(float), float prior, float evidence);

Description​

The UxHwDoubleBayesLaplace function returns the result of the Bayes-Laplace rule applied to the distribution associated with the evidence value, given the prior distribution associated with prior value and the likelihood conditional distribution associated with function pointer likelihood.

Bayes-Laplace rule is computed using:

fH∣E=e(h)=fE∣H=h(e)fH(h)∫fE∣H=x(e)fH(x) dxf_{H \mid E=e}(h) = \frac{f_{E \mid H=h}(e) f_H(h)}{\int f_{E| H = x}(e) f_H(x)\,dx}

where

  • the evidence is ee
  • the prior is fHf_H
  • the likelihood is fE∣Hf_{E|H}
  • and the posterior is fH∣E=ef_{H|E=e}

Parameters​

  • likelihood — The function pointer to the likelihood function in the Bayes-Laplace rule.
  • prior — The prior distribution in the Bayes-Laplace rule.
  • evidence — The evidence distribution in the Bayes-Laplace rule.

Return Values​

The UxHwDoubleBayesLaplace function returns the value associated with the posterior value of the Bayes-Laplace rule.

✏️   Examples​

#include <stdio.h>
#include <uxhw.h>

/*
 *  This function models a sensor which readings are subject to a Gaussian noise.
 */
double
noisySensor(double measurand)
{
    return UxHwDoubleGaussDist(measurand, 0.2);
}

int
main(int argc, char * argv[])
{
    double prior = UxHwDoubleUniformDist(0.0, 2.0);
    printf("prior = %lf\n", prior);

    double evidence = 0.5;

    double posterior = UxHwDoubleBayesLaplace(&noisySensor, prior, evidence);
    printf("posterior = %lf\n", posterior);

    return 0;
}