In categorical data analysis, the contingency tables are commonly used to assess the association between groups and responses, this is achieved by using some measures of association, such as the contingency coefficient, odds ratio, risk relative, etc. In a Bayesian approach, the risk ratio is modeled according to a Beta-Binomial model, which has exact posterior distribution, due to the conjugacy property of the model. In this work, we provide the exact posterior distribution of the relative risk for the non-conjugate Kumaraswamy–Binomial model. The results are based on special functions and we give exact expressions for the posterior density, moments, and cumulative distribution. An example illustrates the theory.
Accepted:
Published online:
Jose A. A. Andrade 1; Pushpa Rathie 2
@article{CRMATH_2023__361_G6_1063_0, author = {Jose A. A. Andrade and Pushpa Rathie}, title = {Exact {Posterior} distribution of risk ratio in the {Kumaraswamy{\textendash}Binomial} model}, journal = {Comptes Rendus. Math\'ematique}, pages = {1063--1069}, publisher = {Acad\'emie des sciences, Paris}, volume = {361}, year = {2023}, doi = {10.5802/crmath.469}, language = {en}, }
TY - JOUR AU - Jose A. A. Andrade AU - Pushpa Rathie TI - Exact Posterior distribution of risk ratio in the Kumaraswamy–Binomial model JO - Comptes Rendus. Mathématique PY - 2023 SP - 1063 EP - 1069 VL - 361 PB - Académie des sciences, Paris DO - 10.5802/crmath.469 LA - en ID - CRMATH_2023__361_G6_1063_0 ER -
Jose A. A. Andrade; Pushpa Rathie. Exact Posterior distribution of risk ratio in the Kumaraswamy–Binomial model. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1063-1069. doi : 10.5802/crmath.469. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.469/
[1] Bayesian Risk Ratio Analysis, Am. Stat., Volume 35 (1981) no. 4, pp. 254-257 | MR
[2] Bayesian analysis of contingency tables from comparative trials, 2003
[3] Exact posterior computation for the binomial-Kumaraswamy model, Adv. Comput. Math., Volume 46 (2020) no. 6, 80, 13 pages | MR | Zbl
[4] On exact posterior distributions using H-functions, J. Comput. Appl. Math., Volume 290 (2015), pp. 459-475 | DOI | MR | Zbl
[5] Exact Posterior Computation in Non-Conjugate Gaussian Location-Scale Parameters Models, Commun. Nonlinear Sci. Numer. Simul., Volume 53 (2017), pp. 111-129 | DOI | MR | Zbl
[6] Exact Bayesian computation using H-functions, Comput. Appl. Math., Volume 38 (2018), pp. 2277-2293 | DOI | MR | Zbl
[7] Estimation of reservoir yield and storage distribution using moments analysis, J. Hydrol., Volume 182 (1996) no. 1-4, pp. 259-275 | DOI
[8] The and functions as symmetrical Fourier kernels, Trans. Am. Math. Soc., Volume 98 (1961), pp. 395-429 | MR | Zbl
[9] A generalized probability density function for double-bounded random processes, J. Hydrol., Volume 46 (1980) no. 1-2, pp. 79-88 | DOI
[10] The Special Functions and Their Approximations, Academic Press Inc., 1979
[11] Bayesian Analysis of a Contingency Table with Both Completely and Partially Cross-Classified Data, J. Educ. Stat., Volume 10 (1985) no. 1, pp. 31-43 | DOI
Cited by Sources:
Comments - Policy