Paired Comparison Model: A Bayesian Non-Informative Analysis
[1]
Sadia Qamar, Department of Statistics, University of Sargodha, Sargodha, Pakistan.
[2]
Amna Nazeer, School of Mathematics and Statistics, Hua Zhong University of Science and Technology, Wuhan, China.
[3]
Samina Satti, Department of Statistics, University of Wah, Wah Cantt, Pakistan.
Application of Bayesian inferential methods has become very appealing to almost every area of research. The current study also focuses on the Bayesian analysis of the van Baaren model-IV for paired comparisons. Use of prior information in form of probability distribution to update the available information is the key step of Bayesian analysis. We have considered the non-informative uniform prior for the analysis of the paired comparison model. Along with the treatment parameters the model also contains threshold or tie parameter and with-in pair order effect parameter. The joint posterior distribution is derived and evaluated to obtain the posterior means, posterior modes and posterior standard deviations. To deal with the estimation of multiparameters the Gibbs sampling scheme was used. The results supported the presence of the with-in pair order effect and the treatment presented first in the comparison of the pair had an advantage of being preferred. The preference and posterior probabilities also validated the findings of the posterior estimates.
Paired Comparison Model, Bayesian Inference, Uniform Prior
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