A Bayesian One-Sample Test for Proportion

Abstract

This paper deals with a new Bayesian approach to the one-sample test for proportion. More specifically, let (Formula presented.) be an independent random sample of size n from a Bernoulli distribution with an unknown parameter (Formula presented.). For a fixed value (Formula presented.), the goal is to test the null hypothesis (Formula presented.) against all possible alternatives. The proposed approach is based on using the well-known formula of the Kullback–Leibler divergence between two binomial distributions chosen in a certain way. Then, the difference of the distance from a priori to a posteriori is compared through the relative belief ratio (a measure of evidence). Some theoretical properties of the method are developed. Examples and simulation results are included.