A Bayesian One-Sample Test for Proportion.

This paper deals with a new Bayesian approach to the one-sample test for proportion. More specifically, let x = (x 1 , ... , x n) be an independent random sample of size n from a Bernoulli distribution with an unknown parameter θ. For a fixed value θ 0 , the goal is to test the null hypothesis H 0 : θ = θ 0 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. [ABSTRACT FROM AUTHOR]