Abstract The matching problem is known since the beginning of the eighteenth century and Bayesian solutions have been proposed. In this paper, we present a Bayesian analysis of an experiment that also leads to the matching problem. Since in this paper we consider the order in which assignments are made and not only the number of matches, our approach is different from the literature on this problem. Our approach also considers that it is possible to have different abilities for the different objects that will be guessed. Hence, we have a parameter that measures the matching ability for each specific object or assignment. As a consequence, we need to have some replicates of the experiment and a prior distribution for each of the parameters. Conjugate prior distributions for the parameters are discussed. The frequentist solution has a particular Bayesian interpretation under a non-informative prior distribution. A real data set is analyzed using the proposed methodology.

中文翻译：

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匹配问题的贝叶斯分析

摘要 匹配问题自 18 世纪初就已为人所知，并提出了贝叶斯解决方案。在本文中，我们对一个也导致匹配问题的实验进行了贝叶斯分析。由于在本文中我们考虑了分配的顺序而不仅仅是匹配的数量，我们的方法与关于这个问题的文献不同。我们的方法还考虑到，对于将要猜测的不同对象，可能具有不同的能力。因此，我们有一个参数来衡量每个特定对象或任务的匹配能力。因此，我们需要对实验进行一些重复，并对每个参数进行先验分布。讨论了参数的共轭先验分布。频率论解决方案在非信息先验分布下具有特定的贝叶斯解释。使用所提出的方法分析真实数据集。