Bayesian Analysis of Rank Data with Covariates and Heterogeneous Rankers
Bayesian Analysis of Rank Data with Covariates and Heterogeneous Rankers
复制标题
含协变量和异质等级数据的贝叶斯分析
DOI：
10.1214/20-sts818
复制
发表时间：
2022-02-01
影响因子：
5.7
通讯作者：
Liu, Jun S.
中科院分区：
文献类型：
--
作者：
Li, Xinran;Yi, Dingdong;Liu, Jun S.
经常会遇到排名列表形式的数据，并且组合来自不同来源的排名结果可以潜在地生成更好的排名列表并帮助理解排名者的行为。这里感兴趣的是以下设置下的排名数据：（i）可用于排名实体的协变量信息;（ii）不同质量或具有不同意见的排名者;以及（iii）非重叠子组的不完整排名列表。我们回顾了过去几十年来研究人员围绕Thurstone模型家族构建的一些关键思想，并提供了一种统一的方法，用于协变量的贝叶斯秩数据分析（BARC）及其扩展，用于处理异质秩。在贝叶斯框架下，我们可以研究排名者的不同质量，聚类排名者的异质性意见，并测量相应的不确定性。为了实现高效的贝叶斯推理，我们主张使用参数扩展的吉布斯采样器从目标后验分布中进行采样。后验样本还导致贝叶斯聚合排名列表，可信区间量化其不确定性。我们调查和比较所提出的方法和其他秩聚合方法在模拟研究和两个真实数据的例子中的性能。
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 nonover-lapping 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.