Bayesian Analysis of the Rayleigh Paired Comparison Model under Loss Functions using Informative Prior

Document Type: Research Note

Authors

1 Department of Mathematics and Statistics, Riphah International University, Islamabad, Pakistan

2 Department of Statistics, Quaid-i-Azam University, Islamabad,Pakistan

Abstract

A number of paired comparison (PC) models exists in the literature. In this paper, the posterior
distribution of the parameters of the Rayleigh PC model is derived using informative prior: Conjugate and
Dirichlet. The values of the hyperparameters are elicited using prior predictive distribution. The preferences
for the data of cigarette brands: Goldleaf (GL), Marlboro (ML), Dunhill (DH) and Benson & Hedges (BH)
are collected from university students. 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 calculated. The posterior
probabilities, for the hypothesis of comparing two parameters are evaluated. The graphs of marginal
posterior distributions are given. Appropriateness of the model is tested by Chi-Square.

Main Subjects