Many modern experiments, such as microarray gene expression and genome-wide association studies, present the problem of estimating a large number of parallel effects. Bayesian inference is a popular approach for analyzing such data by modeling the large number of unknown parameters as random effects from a common prior distribution. However, misspecification of the prior distribution, particularly in the tails of the distribution, can lead to erroneous estimates of the random effects, especially for the largest and most interesting effects. This paper proposes a robustified posterior distribution that eliminates the impact of a misspecified prior on one component of the standard posterior by replacing that component with an asymptotically correct form. The proposed posterior can be combined with a flexible working prior to achieve superior inference across different structures of the underlying effects of interest.

中文翻译：

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大量并行效应的贝叶斯推理的稳健后验

许多现代实验，例如微阵列基因表达和全基因组关联研究，都存在估计大量平行效应的问题。贝叶斯推理是一种流行的分析此类数据的方法，它通过将大量未知参数建模为来自共同先验分布的随机效应。然而，先验分布的错误指定，特别是在分布的尾部，可能导致对随机效应的错误估计，尤其是对于最大和最有趣的效应。本文提出了一种稳健的后验分布，通过用渐近正确的形式替换该组件来消除错误指定的先验对标准后验的一个组件的影响。