  Data in the form of ranking lists are frequently encountered, and combining
ranking results from different sources can potentially generate a better
ranking list and help understand behaviors of the rankers. Of interest here are
the rank data under the following settings: (i) covariate information available
for the ranked entities; (ii) rankers of varying qualities or having different
opinions; and (iii) incomplete ranking lists for non-overlapping subgroups. We
review some key ideas built around the Thurstone model family by researchers in
the past few decades and provide a unifying approach for Bayesian Analysis of
Rank data with Covariates (BARC) and its extensions in handling heterogeneous
rankers. With this Bayesian framework, we can study rankers' varying quality,
cluster rankers' heterogeneous opinions, and measure the corresponding
uncertainties. To enable an efficient Bayesian inference, we advocate a
parameter-expanded Gibbs sampler to sample from the target posterior
distribution. The posterior samples also result in a Bayesian aggregated
ranking list, with credible intervals quantifying its uncertainty. We
investigate and compare performances of the proposed methods and other rank
aggregation methods in both simulation studies and two real-data examples.
