论文标题
在反回归问题中选择模型选择的贝叶斯多重测试范例
A Bayesian Multiple Testing Paradigm for Model Selection in Inverse Regression Problems
论文作者
论文摘要
在本文中，我们提出了一种新型的贝叶斯多重测试公式，用于模型和反向设置中的可变选择，明智地将Bhattacharya（2013）提出的反参考分布的概念嵌入了由竞争模型组成的混合框架中。我们在涵盖参数和非参数竞争模型的一般环境中开发理论和方法，依赖数据以及不明显。我们的研究表明，渐近多重测试程序几乎可以肯定地选择了最佳的逆模型，从而最大程度地减少了与真实模型的最小kullback-leibler差异。我们还表明，错误率，即错误发现率的版本和错误的非发现速率，几乎肯定会在样本量变为Infinity时肯定会收敛到零。还研究了错误发现率的版本的渐近α控制及其对错误非发现率版本的收敛性的影响。 我们的仿真实验涉及在反泊泊托型记录回归和逆几何logit和概率回归中基于样本的小选择，其中回归是线性的，要么基于高斯过程。另外，还考虑了变量选择。在所有非固定案例中选择最佳模型的意义上，我们的多次测试结果非常令人鼓舞。
In this article, we propose a novel Bayesian multiple testing formulation for model and variable selection in inverse setups, judiciously embedding the idea of inverse reference distributions proposed by Bhattacharya (2013) in a mixture framework consisting of the competing models. We develop the theory and methods in the general context encompassing parametric and nonparametric competing models, dependent data, as well as misspecifications. Our investigation shows that asymptotically the multiple testing procedure almost surely selects the best possible inverse model that minimizes the minimum Kullback-Leibler divergence from the true model. We also show that the error rates, namely, versions of the false discovery rate and the false non-discovery rate converge to zero almost surely as the sample size goes to infinity. Asymptotic α-control of versions of the false discovery rate and its impact on the convergence of false non-discovery rate versions, are also investigated. Our simulation experiments involve small sample based selection among inverse Poisson log regression and inverse geometric logit and probit regression, where the regressions are either linear or based on Gaussian processes. Additionally, variable selection is also considered. Our multiple testing results turn out to be very encouraging in the sense of selecting the best models in all the non-misspecified and misspecified cases.
