Eliciting hyperparameters of prior distributions for the parameters of paired comparison models

Abstract

In the study of paired comparisons (PC), items may be ranked or issues may be prioritized through subjective assessment of certain judges. PC models are developed and then used to serve the purpose of ranking. The PC models may be studied through classical or Bayesian approach. Bayesian inference is a modern statistical technique used to draw conclusions about the population parameters. Its beauty lies in incorporating prior information about the parameters into the analysis in addition to current information (i.e. data). The prior and current information are formally combined to yield a posterior distribution about the population parameters, which is the work bench of the Bayesian statisticians. However, the problems the Bayesians face correspond with the selection and formal utilization of prior distribution. Once the type of prior distribution is decided to be used, the problem of estimating the parameters of the prior distribution (i.e. elicitation) still persists. Different methods are devised to serve the purpose. In this study an attempt is made to use Minimum Chi-square (hence forth MCS) for the elicitation purpose. Though it is a classical estimation technique, it is used here for the elicitation purpose. The entire elicitation procedure is illustrated by a real data set.

Bayesian modeling to paired comparison data via the Pareto distribution

“…Here Now it is vital to elicit a value for the parameter α that best suits a certain data set. To accomplish this, we have used the minimum chi-square method suggested by Abbas and Aslam (2013). It is inferred therein that α = 0.55 produced minimum chi-square value for the given data set and is hence used in the subsequent analyses.…”