On the interpretation and the choice of the hyperparameters of a beta prior distribution

Binary outcomes are frequently encountered in a variety of fields and contexts and the Bayesian approach is widely used to analyse this type of data. Under this framework, a beta prior distribution for the probability of success is typically used. We clarify why in the statistical literature one can find two slightly different interpretations of the prior hyperparameters as extra data. The two interpretations can be exploited to elicit informative beta prior densities by specifying a measure of central tendency and a suitable value for the prior sample size. We developed a Shiny App in R that provides a user-friendly interface to implement the elicitation procedures.