论文标题
使用Dirichlet过程和Beta-Binomial模型先验的灵活贝叶斯多重比较调整
Flexible Bayesian Multiple Comparison Adjustment Using Dirichlet Process and Beta-Binomial Model Priors
论文作者
论文摘要
研究人员经常希望评估群体的平等或不平等，但这构成了对多次比较进行充分调整的挑战。从统计上讲，所有可能的平等和不等式约束的配置都可以独特地表示为组的分区，如果组在分区的同一子集中，则任何数量的组都相等。在贝叶斯框架中，可以通过在所有可能的分区上构造合适的先验分布来调整多个比较。受回归中可变选择的工作的启发，我们提出了一类灵活的β-二项制先验，以进行多次比较调整。我们将此先前的设置与Gopalan和Berry（1998）提出的事先提出的Dirichlet过程和多次比较调整方法进行了比较，该方法未直接指定先前的分区。我们的方法不仅允许研究人员评估成对的平等约束，而且可以同时评估所有群体之间所有可能的平等性。由于可能分区的空间迅速增长 - 对于十组，已经有115,975个可能的分区 - 我们使用随机搜索算法有效地探索该空间。我们的方法是在Julia软件包相等漫画中实现的，我们以与均值，标准偏差和比例的比较有关的示例进行了说明。
Researchers frequently wish to assess the equality or inequality of groups, but this poses the challenge of adequately adjusting for multiple comparisons. Statistically, all possible configurations of equality and inequality constraints can be uniquely represented as partitions of groups, where any number of groups are equal if they are in the same subset of the 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 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 not only allows researchers to assess pairwise equality constraints but simultaneously all possible equalities among all groups. Since the space of possible partitions grows rapidly -- for ten groups, there are already 115,975 possible partitions -- we use 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, standard deviations, and proportions.
