Bayesian analysis of the Rayleigh paired comparison model under loss functions using an informative prior

Considering a number of Paired Comparison (PC) models existing in the literature, the posterior distribution for the parameters of the Rayleigh PC model is derived in this paper using the informative priors: Conjugate and Dirichlet. The values of the hyperparameters are elicited using prior predictive distribution. The preferences for the data of cigarette brands, such as Goldleaf (GL), Marlboro (ML), Dunhill (DH), and Benson & Hedges (BH), are collected based on university studentsʹ opinions. The posterior estimates of the parameters are obtained under the loss functions: Quadratic Loss Function (QLS), Weighted Loss Function (WLS), and Squared Error Loss Function (SELF) with their risks. The preference and predictive probabilities are investigated. The posterior probabilities are evaluated with respect to the hypotheses of two parameters comparison. In this respect, the graphs of marginal posterior distributions are presented, and appropriateness of the model is tested by Chi-Square