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Assessing Multinomial Distributions with a Bayesian Approach

Author

Listed:
  • Luai Al-Labadi

    (Department of Mathematical & Computational Sciences, University of Toronto Mississauga, Toronto, ON L5L 1C6, Canada)

  • Petru Ciur

    (Department of Mathematical & Computational Sciences, University of Toronto Mississauga, Toronto, ON L5L 1C6, Canada)

  • Milutin Dimovic

    (Department of Mathematical & Computational Sciences, University of Toronto Mississauga, Toronto, ON L5L 1C6, Canada)

  • Kyuson Lim

    (Department of Mathematics & Statistics, McMaster University, 1280 Main Street West, Hamilton, ON L8S 4L8, Canada)

Abstract

This paper introduces a unified Bayesian approach for testing various hypotheses related to multinomial distributions. The method calculates the Kullback–Leibler divergence between two specified multinomial distributions, followed by comparing the change in distance from the prior to the posterior through the relative belief ratio. A prior elicitation algorithm is used to specify the prior distributions. To demonstrate the effectiveness and practical application of this approach, it has been applied to several examples.

Suggested Citation

  • Luai Al-Labadi & Petru Ciur & Milutin Dimovic & Kyuson Lim, 2023. "Assessing Multinomial Distributions with a Bayesian Approach," Mathematics, MDPI, vol. 11(13), pages 1-16, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:3007-:d:1188009
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    References listed on IDEAS

    as
    1. Alan Agresti & Yongyi Min, 2005. "Frequentist Performance of Bayesian Confidence Intervals for Comparing Proportions in 2 × 2 Contingency Tables," Biometrics, The International Biometric Society, vol. 61(2), pages 515-523, June.
    2. Luai Al-Labadi, 2021. "The two-sample problem via relative belief ratio," Computational Statistics, Springer, vol. 36(3), pages 1791-1808, September.
    3. Alan Agresti & David B. Hitchcock, 2005. "Bayesian inference for categorical data analysis," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 14(3), pages 297-330, December.
    4. Ostrovski, Vladimir, 2017. "Testing equivalence of multinomial distributions," Statistics & Probability Letters, Elsevier, vol. 124(C), pages 77-82.
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