The Rayleigh paired comparison model with Bayesian analysis

Year 2016, Volume: 45 Issue: 5, 1541 - 1552, 01.10.2016

Tanveer Kifayat Muhammad Aslam

Abstract

A paired comparison (PC) method is more reliable to rank or compare more than two items/ objects at the same time. It is a welldeveloped method of ordering attributes or characteristics of a given set of items.The PC model is developed using Rayleigh random variables on the basis of Stern's criteria [17]. The Rayleigh PC model is analyzed in Bayesian framework using non-informative (Jeffreys and Uniform) priors. The Bayesian inference of the developed model is compared with existing the Bradley-Terry model. The preference and predictive probabilities for current and future comparisons are calculated. The posterior probabilities of hypotheses for comparing two parameters are evaluated. The Bayesian 95% credible interval are calculated.Appropriateness of the model is also examined. Graphs of marginal posterior distributions of the parameters are drawn. The Bayesian analysis is performed using real life data sets.

Keywords

Paired Comparisons, Rayleigh Distribution, Non-Informative Prior, Posterior Probability, Predictive Probability

References

• [17] Stern, H. A continuum of paird comparisons models, Biometrtsika, 77 (2), 265-273, 1990.