标题： 贝叶斯公平：奥运奖牌榜的贝叶斯排名 显示英文标题

标题： Bayes-ically fair: A Bayesian Ranking of the Olympic Medal Table

摘要： 评估一个国家的体育成功情况可以深入了解其在培养运动员人才方面的决策和基础设施。 奥林匹克运动会作为全球基准，但传统的奖牌排名可能受到人口规模的不当影响。 我们提出了一种贝叶斯排名方案，通过其“长期”奖牌与人口比率对国家奥林匹克委员会的表现进行排名。 该算法旨在通过应用收缩方法，减轻大人口的影响，并减少小国的随机波动。 这些长期排名相比现有方法，提供了更稳定且易于解释的国家体育表现排序。 显示英文摘要

摘要： Evaluating a country's sporting success provides insight into its decision-making and infrastructure for developing athletic talent. The Olympic Games serve as a global benchmark, yet conventional medal rankings can be unduly influenced by population size. We propose a Bayesian ranking scheme to rank the performance of National Olympic Committees by their "long-run" medals-to-population ratio. The algorithm aims to mitigate the influence of large populations and reduce the stochastic fluctuations for smaller nations by applying shrinkage. These long-run rankings provide a more stable and interpretable ordering of national sporting performance across games compared to existing methods.