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 theta. For a fixed value theta(0), the goal is to test the null hypothesis H-0:theta-theta(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.