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Bayesian Statistics: An Introduction, 4th Edition by Peter M. Lee

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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

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from a binomial distribution of index n and parameter π, and so

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The binomial distribution was introduced in Section 1.3 on ‘Random Variables’ and its properties are of course summarized in Appendix A.

Figure 3.1 Examples of beta densities.

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If your prior for π has the form

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that is, if

Unnumbered Display Equation

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