Bayesian Analysis of Rank Data with Covariates and Heterogeneous Rankers

Data in the form of ranking lists are frequently encountered, and combining ranking results from different sources can potentially generatea better ranking list and help understand behaviors of the rankers. Of interesthere are the rank data under the following settings: (i) covariate informationavailable for the ranked entities; (ii) rankers of varying qualitiesor having different opinions; and (iii) incomplete ranking lists for nonoverlappingsubgroups. We review some key ideas built around the Thurstonemodel family by researchers in the past few decades and provide a unifyingapproach for Bayesian Analysis of Rank data with Covariates (BARC) andits extensions in handling heterogeneous rankers. With this Bayesian framework,we can study rankers’ varying quality, cluster rankers’ heterogeneousopinions, and measure the corresponding uncertainties. To enable an efficientBayesian inference, we advocate a parameter-expanded Gibbs samplerto sample from the target posterior distribution. The posterior samples alsoresult in a Bayesian aggregated ranking list, with credible intervals quantifyingits uncertainty.We