论文标题
贝叶斯多重测试程序的高维渐近理论在普遍的依赖设置和可能的错误指定下
High-dimensional Asymptotic Theory of Bayesian Multiple Testing Procedures Under General Dependent Setup and Possible Misspecification
论文作者
论文摘要
在本文中，当样本量和假设的数量均倾向于无穷大时，我们研究了贝叶斯多重测试程序的渐近性能。具体而言，我们研究了在高维设置下的不同版本的错误发现和错误的非发现速率的程序和渐近特性的强大一致性。我们特别关注一种新型的贝叶斯非分支多重测试程序及其在这方面的相关错误率。我们的结果表明，错误率的渐近收敛速率与真实模型的Kullback-Leibler差异直接相关，即使在误指定的假定模型类别时，结果也会成立。为了说明我们的高维渐近理论，我们在随时间变化的协变量选择框架中考虑了贝叶斯变量选择问题，并具有自回归响应变量。我们特别关注的是，与样本量相比，假设的数量以更快的速度增加的设置，即所谓的超高维情况。
In this article, we investigate the asymptotic properties of Bayesian multiple testing procedures under general dependent setup, when the sample size and the number of hypotheses both tend to infinity. Specifically, we investigate strong consistency of the procedures and asymptotic properties of different versions of false discovery and false non-discovery rates under the high dimensional setup. We particularly focus on a novel Bayesian non-marginal multiple testing procedure and its associated error rates in this regard. Our results show that the asymptotic convergence rates of the error rates are directly associated with the Kullback-Leibler divergence from the true model, and the results hold even when the postulated class of models is misspecified. For illustration of our high-dimensional asymptotic theory, we consider a Bayesian variable selection problem in a time-varying covariate selection framework, with autoregressive response variables. We particularly focus on the setup where the number of hypotheses increases at a faster rate compared to the sample size, which is the so-called ultra-high dimensional situation.
