February 2022 Bayesian Analysis of Rank Data with Covariates and Heterogeneous Rankers
Xinran Li, Dingdong Yi, Jun S. Liu
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Statist. Sci. 37(1): 1-23 (February 2022). DOI: 10.1214/20-STS818


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 nonoverlapping 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.


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Xinran Li. Dingdong Yi. Jun S. Liu. "Bayesian Analysis of Rank Data with Covariates and Heterogeneous Rankers." Statist. Sci. 37 (1) 1 - 23, February 2022. https://doi.org/10.1214/20-STS818


Published: February 2022
First available in Project Euclid: 19 January 2022

MathSciNet: MR4369087
zbMATH: 07474195
Digital Object Identifier: 10.1214/20-STS818

Keywords: heterogeneous rankers , infinite mixture model , parameter-expanded data augmentation , rank aggregation , Thurstone model

Rights: Copyright © 2022 Institute of Mathematical Statistics


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Vol.37 • No. 1 • February 2022
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