Bayesian Interpretation of Frequentist Procedures for a Bernoulli Process

Abstract

In considering the inference about the unknown proportion of a Bernoulli process, it is shown that the choices involved in the frequentist approach are equivalent, from a Bayesian point of view, to the choice of a particular ignorance prior within a restricted ignorance zone. This link sheds light on the nature of both kinds of choices, and on undesirable properties that go with null variance data.

Key Words:

• Binary data
• Correction for continuity
• Ignorance zone
• Inclusive/exclusive convention
• Noninformative prior
• One-sided significance test
• Reference Bayesian approach
• Stopping rule.