Bayesian analysis of the amended Davidson model for paired comparison using noninformative and informative priors

Abstract

In recent years, numerous statisticians have focused their attention on the Bayesian analysis of different paired comparison models. While studying paired comparison techniques, the Davidson model is considered to be one of the famous paired comparison models in the available literature. In this article, we have introduced an amendment in the Davidson model which has been commenced to accommodate the option of not distinguishing the effects of two treatments when they are compared pairwise. Having made this amendment, the Bayesian analysis of the Amended Davidson model is performed using the noninformative (uniform and Jeffreys’) and informative (Dirichlet–gamma–gamma) priors. To study the model and to perform the Bayesian analysis with the help of an example, we have obtained the joint and marginal posterior distributions of the parameters, their posterior estimates, graphical presentations of the marginal densities, preference and predictive probabilities and the posterior probabilities to compare the treatment parameters.

Keywords:

• Bayesian analysis
• Bayes factor
• Davidson model
• paired comparison models
• noninformative priors

AMS Classification: :

• 62A15

Notes

The confidence levels are assumed to be very small as we are considering many intervals at a time.