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 x=(x1,…,xn) be an independent random sample of size n from a Bernoulli distribution with an unknown parameter θ. For a fixed value θ0, the goal is to test the null hypothesis H0:θ=θ0 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.

Assessing Multinomial Distributions with a Bayesian Approach

“…We build on the recent work of [27] by extending their Bayesian approach for hypothesis testing on one-sample proportions based on Kullback-Leibler divergence and relative belief ratio, using a uniform (0, 1) prior on binomial proportions, to multinomial distributions. Our goal is to provide a comprehensive Bayesian approach for testing hypotheses H 1 0 , H 2 0 , and H 3 0 .…”