On the Certainty of an Inductive Inference: The Binomial Case

Abstract

In the context of the binomial distribution, the potential need for a prior point mass on $\mathit{\theta }=0(1)$, given $\mathit{x}=0(\mathit{n})$, was identified more than 100 years ago by Jeffreys. Given previous proposals to implement such a point mass, a slightly different approach is proposed, followed by the corresponding posterior probability of “homogeneity” and posterior predictive distribution.