Bayesian Approach to Statistical Treatment

The Bayes distribution or the posterior probability density function Fpos(0 fc), which serves the evaluation of Bis, is  

Here L(k 0) is the likelihood of observing the concrete data k given the parameter value. The pdf-like /yiC ) is a non-negative function called prior distribution, the choice of which is discussed below. The integration is performed over the range of the prior distribution. 

When the parameter is a discrete quantity, Eq. 6.2 should be consistently rewritten for summation  

For example, if k decays or a rare short-lived nuclide were detected in the course of a long bombardment and we need to know the Bayesian confidence interval for the yield rate (per the duration of the bombardment) 0, then L(k ) is the Poisson distribution  

In another common problem, 0 is the number of radioactive nuclei which were originally present in a sample and gave k counts when measured with the detection efficiency px until they decayed. Now the likelihood is given by the binomial distribution  

---