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Exact Posterior Inferences for the Odds Ratio in the Binomial–Kumaraswamy Model |
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PP: 7-14 |
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doi:10.18576/amisl/130102
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Author(s) |
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J. A. A. Andrade,
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Abstract |
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| The class of contingency 2×2 tables is an important tool for checking the association between two qualitative variables. Among the several measures of association, the odds ratio is perhaps the most prominent due to its elegant mathematical properties. A common Bayesian model for the odds ratio uses the Beta-Binomial model, which is conjugate, in the sense that the posterior distribution is also a Beta distribution. Although the posterior inferences are exact, the Beta distribution could be replaced by other distributions within the interval (0,1), such as the Kumaraswamy, which has been extensively used in the past few decades. However, the Kumaraswamy-Binomial model is not conjugate, which would require the use of approximate methods. In this work, we show that we can obtain the posterior inferences for the odds ratio in an exact form; that is, we provide explicit and computable forms for the posterior distribution and its quantities. An application is provided comparing cancer screening tests. |
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