Efficient Bayesian Inference for Benter Models on Ranked Data

2026-08-24

AI Summary

本文提出了一种高效的贝叶斯估计方法，通过引入辅助变量线性化Benter模型中的不可解标准化项，解决了该模型拟合的挑战。

Abstract

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.

Problem

• Bayesian Inference
• Benter Model
• Ranked Data
• Dampening Parameters
• Likelihood

Innovation

• Bayesian Inference
• Benter Model
• Augmentation Scheme
• Gibbs Updates