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A Bayesian One-Sample Test for Proportion

Author

Listed:
  • 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)

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.

Suggested Citation

  • Luai Al-Labadi & Yifan Cheng & Forough Fazeli-Asl & Kyuson Lim & Yanqing Weng, 2022. "A Bayesian One-Sample Test for Proportion," Stats, MDPI, vol. 5(4), pages 1-12, December.
    • Handle: RePEc:gam:jstats:v:5:y:2022:i:4:p:75-1253:d:990293
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    References listed on IDEAS

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    1. Luai Al-Labadi, 2021. "The two-sample problem via relative belief ratio," Computational Statistics, Springer, vol. 36(3), pages 1791-1808, September.
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