A bayesian look at the bradley-terry paired comparison model

In the present study, we have presented a statistical analysis for paired comparison data through Bayesian approach. In the method of paired comparisons, objects are presented in pairs to the judges. The Bradley-Terry model for paired comparisons is considered for Bayesian analysis. The prior distribution for the parameters of the model is supposed to be belonged to the member of the Dirichlet family and the method for elicitation of hyperparameters is based on the prior predictive distribution. For Bayesian analysis, the posterior distribution of the parameters is derived, the preference probabilities using the posterior means and the predictive probabilities for pairwise comparisons in a single future comparison are obtained. The posterior probabilities for the hypotheses of comparing two parameters are also computed. The goodness of fit test for the appropriateness of the model is presented too.