标题： 贝塔密度的狄利克雷混合在估计正向错误发现率中的后验一致性 显示英文标题

标题： Posterior consistency of Dirichlet mixtures of beta densities in estimating positive false discovery rates

摘要： 近年来，多重假设检验已成为统计研究的前沿，显然与基因组学和其他一些新兴领域的应用有关。 错误发现率（FDR）及其变体在此背景下提供了非常重要的误差概念，类似于经典检验问题中误差概率的作用。 准确估计正向FDR（pFDR），FDR的一个变体，在评估和控制这一指标中至关重要。 在最近的一篇论文中，作者提出了一种基于模型的非参数贝叶斯方法来估计pFDR函数。 特别是，p值的密度被建模为递减的beta密度的混合，并考虑了一个适当的Dirichlet过程作为混合度量的先验。 该方法在模拟中表现良好。 在本文中，我们提供了一些理论结果，以支持p值密度的beta混合模型，并表明在适当条件下，随着假设数量趋于无穷大，所得后验是一致的。 显示英文摘要

摘要： In recent years, multiple hypothesis testing has come to the forefront of statistical research, ostensibly in relation to applications in genomics and some other emerging fields. The false discovery rate (FDR) and its variants provide very important notions of errors in this context comparable to the role of error probabilities in classical testing problems. Accurate estimation of positive FDR (pFDR), a variant of the FDR, is essential in assessing and controlling this measure. In a recent paper, the authors proposed a model-based nonparametric Bayesian method of estimation of the pFDR function. In particular, the density of p-values was modeled as a mixture of decreasing beta densities and an appropriate Dirichlet process was considered as a prior on the mixing measure. The resulting procedure was shown to work well in simulations. In this paper, we provide some theoretical results in support of the beta mixture model for the density of p-values, and show that, under appropriate conditions, the resulting posterior is consistent as the number of hypotheses grows to infinity.