Department of Mathematical & Computational Sciences, University of Toronto Mississauga, Mississauga, ON L5L 1C6, Canada
Yifan Cheng
Department of Mathematical & Computational Sciences, University of Toronto Mississauga, Mississauga, ON L5L 1C6, Canada
Forough Fazeli-Asl
Department of Statistics & Actuarial Science, University of Hong Kong, Pok Fu Lam, Hong Kong
Kyuson Lim
Department of Mathematics & Statistics, McMaster University, 1280 Main St. W, Hamilton, ON L8S 4L8, Canada
Yanqing Weng
Department of Mathematics & Department of Statistical Sciences, University of Toronto St. George, 27 King’s College Circle, Toronto, ON M5S 1A4, Canada
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.
