针对排序数据的本特（Benter）模型的高效贝叶斯推断
Efficient Bayesian Inference for Benter Models on Ranked Data
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中文总结 AI 辅助
该研究针对本特（Benter）模型拟合的挑战，提出基于α稳定和指数辅助变量的两部分增广方案，实现高效贝叶斯估计，经模拟与真实排序数据验证，可准确恢复参数并覆盖名义可信区间。
中文摘要 AI 辅助
用于部分排序和完全排序的本特（Benter）模型通过附加排序级别的阻尼参数，对著名的普拉克特-卢斯（Plackett-Luce）模型进行了扩展，这些参数允许某些排序阶段比其他阶段更具噪声。这种扩展在从赛马到排序选择选举等领域具有重要的实证意义。然而，这些阻尼参数为似然函数引入的分数幂使得模型拟合极具挑战性，破坏了现有普拉克特-卢斯采样器所依赖的共轭性。本文开发了一种用于本特（Benter）模型的高效贝叶斯估计方法，引入了一种由正α稳定变量和指数辅助变量组成的两部分增广方案，该方案可线性化本特（Benter）似然中难以处理的归一化常数，并产生闭式吉布斯更新。模拟研究证实，该方法在各种样本量和项目数量下均能实现高效估计、准确的参数恢复以及名义可信区间覆盖率。我们在来自调查偏好和排序选择选举数据集的完全排序与部分排序数据上对该算法进行了演示。
英文摘要
The Benter model for partial and complete rankings generalizes the well-known Plackett-Luce by attaching rank-level dampening parameters that permit some ranking stages to be noisier than others. This extension is empirically important for domains ranging from horse racing to ranked-choice elections. However, model fitting is made challenging by the fractional powers these dampening parameters introduce to the likelihood, breaking the conjugacy underlying existing Plackett-Luce samplers. This paper develops an efficient Bayesian estimation procedure for the Benter model. We introduce a two-part augmentation scheme using positive $α$-stable and exponential auxiliary variables that linearizes the intractable normalizers in the Benter likelihood and yields closed-form Gibbs updates. A simulation study confirms efficient estimation, accurate parameter recovery, and nominal credible-interval coverage across sample sizes and item counts. We illustrate the algorithm on complete and partial rankings from survey preference and ranked-choice election datasets.
