September 2012
Intermediate to advanced
486 pages
10h 41m
English
Content preview from Bayesian Statistics: An Introduction, 4th EditionBecome an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
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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
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