The Counter-intuitive Non-informative Prior for the Bernoulli Family

In Bayesian statistics, the choice of the prior distribution is often controversial. Different rules for selecting priors have been suggested in the literature, which, sometimes, produce priors that are difficult for the students to understand intuitively. In this article, we use a simple heuristic to illustrate to the students the rather counter-intuitive fact that flat priors are not necessarily non-informative; and non-informative priors are not necessarily flat.