标题： 通过贝叶斯镜像统计量进行错误发现率控制 显示英文标题

标题： False Discovery Rate Control via Bayesian Mirror Statistic

摘要： 同时在高维模型中进行变量选择和推断是统计学和机器学习中的一个开放性挑战。 随着大量变量的可用性不断增加，需要采用特定的统计程序，在高维空间中准确选择最重要的预测变量，同时能够控制某种形式的选择误差。 在这项工作中，我们将镜像统计方法用于错误发现率（FDR）控制，适应到贝叶斯建模框架中。 镜像统计是在经典的频率统计框架中开发的，是一种灵活的方法，用于控制FDR，只需较弱的模型假设，但需要两组独立的回归系数估计，通常在分割原始数据集后获得。 在这里，我们提出依赖于模型的贝叶斯表述，并利用感兴趣系数的后验分布来构建镜像统计量，并在不需要分割数据的情况下有效控制FDR。 此外，该方法非常灵活，因为它可以与连续和离散的结果以及更复杂的预测因子一起使用，例如混合模型。 我们通过依靠自动微分变分推断和完全连续先验选择，保持该方法在高维情况下的可扩展性。 显示英文摘要

摘要： Simultaneously performing variable selection and inference in high-dimensional models is an open challenge in statistics and machine learning. The increasing availability of vast amounts of variables requires the adoption of specific statistical procedures to accurately select the most important predictors in a high-dimensional space, while being able to control some form of selection error. In this work we adapt the Mirror Statistic approach to False Discovery Rate (FDR) control into a Bayesian modelling framework. The Mirror Statistic, developed in the classic frequentist statistical framework, is a flexible method to control FDR, which only requires mild model assumptions, but requires two sets of independent regression coefficient estimates, usually obtained after splitting the original dataset. Here we propose to rely on a Bayesian formulation of the model and use the posterior distributions of the coefficients of interest to build the Mirror Statistic and effectively control the FDR without the need to split the data. Moreover, the method is very flexible since it can be used with continuous and discrete outcomes and more complex predictors, such as with mixed models. We keep the approach scalable to high-dimensions by relying on Automatic Differentiation Variational Inference and fully continuous prior choices.