Researchers frequently wish to assess the equality or inequality of groups, but this comes with the challenge of adequately adjusting for multiple comparisons. Statistically, all possible configurations of equality and inequality constraints can be uniquely represented as partitions of the groups, where any number of groups are equal if they are in the same partition. In a Bayesian framework, one can adjust for multiple comparisons by constructing a suitable prior distribution over all possible partitions. Inspired by work on variable selection in regression, we propose a class of flexible beta-binomial priors for Bayesian multiple comparison adjustment. We compare this prior setup to the Dirichlet process prior suggested by Gopalan and Berry (1998) and multiple comparison adjustment methods that do not specify a prior over partitions directly. Our approach to multiple comparison adjustment not only allows researchers to assess all pairwise (in)equalities, but in fact all possible (in)equalities among all groups. As a consequence, the space of possible partitions grows quickly - for ten groups, there are already 115,975 possible partitions - and we set up a stochastic search algorithm to efficiently explore the space. Our method is implemented in the Julia package EqualitySampler, and we illustrate it on examples related to the comparison of means, variances, and proportions.

翻译：研究人员经常希望评估各群体之间的平等或不平等,但与此同时,还需要为多重比较做出适当的调整。从统计学上看,所有可能的平等和不平等制约组合都可以作为各群体之间的分区而具有独特的代表性,如果各群体处于同一分区中,任何数目的分组都是平等的。在巴伊西亚框架内,人们可以通过在所有可能的分区中建立适当的先前分配来调整多种比较。由于在倒退中进行可变选择的工作,我们为巴伊西亚多重比较调整建议了一类灵活的β-binomial前科。我们比较了先前设置的Drichlet进程,Gopalan和Berry(1998年)和多类比较调整方法,这些调整方法没有直接指明先前的分区。我们进行多重比较调整的方法不仅允许研究人员评估所有对齐的(不平等),而且实际上允许所有群体之间的不平等。结果是,可能的分区空间迅速扩大――10个组,可能存在的分区已经存在115,975个可能的分歧——我们为有效探索空间设置了一种随机搜索算法。我们的方法在朱利亚套件中展示了相关的例子。我们的方法是用来进行比较的。