A Bayesian One-Sample Test for Proportion

Luai Al-Labadi (), Yifan Cheng, Forough Fazeli-Asl, Kyuson Lim and Yanqing Weng
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Luai Al-Labadi: 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

Stats, 2022, vol. 5, issue 4, 1-12

Abstract: 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.

Keywords: binomial test; hypothesis testing; prior-data conflict; Kullback–Leibler divergence; relative belief ratio; strength (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2022
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