Bayesian inference on a proportion believed to be a simple fraction.
This article considers the problem of making inference on a proportion when there is reason to believe that the proportion is a simple fraction. By a simple fraction we mean a fraction that, when put in lowest terms, has a small denominator. After discussing the history of Bayesian inference on a proportion, we propose a class of otherwise noninformative priors that incorporates the idea that the proportion is likely to be a simple fraction, and we explore the impact of the choice of parameter. We propose the posterior mode as a point estimator, and we study the behavior of this estimator both asymptotically and for small sample sizes. We illustrate our approach by applying it both to the famous problem of estimating the probability that the sun will rise again tomorrow and to examples from the scientific work of the Augustinian friar Gregor Mendel.
|Main Author:||Frey, Jesse.|