3.1 The binomial distribution
3.1.1 Conjugate prior
In this section, the parameter of interest is the probability π of success in a number of trials which can result in success (S) or failure (F), the trials being independent of one another and having the same probability of success. Suppose that there is a fixed number of n trials, so that you have an observation x (the number of successes) such that
from a binomial distribution of index n and parameter π, and so
The binomial distribution was introduced in Section 1.3 on ‘Random Variables’ and its properties are of course summarized in Appendix A.
If your prior for π has the form
that is, if