论文标题
贝叶斯对广义线性模型中层次非本地先验的推断
Bayesian inference on hierarchical nonlocal priors in generalized linear models
论文作者
论文摘要
在线性回归模型中已广泛研究了具有非局部先验的可变选择方法，并且已经报道了其理论和经验性能。然而，很少研究高维线性回归中分层非局部先验的关键模型选择特性。在本文中，我们考虑了高维Logistic回归模型的分层非本地先验，并研究了后验分布的理论特性。具体而言，在调谐参数上具有逆伽马的回归系数上，施加了乘积矩（PMOM）非局部先验。在标准的规律性假设下，我们在高维设置中建立了强大的模型选择一致性，在该设置中，允许协变量的数量以带有样本量的亚指数速率增加。我们实施用于计算后验概率的拉普拉斯近似，并建议修改的shot弹枪随机搜索步骤有效地探索模型空间。我们通过模拟研究和RNA测序数据集证明了该方法的有效性，以分层疾病风险。
Variable selection methods with nonlocal priors have been widely studied in linear regression models, and their theoretical and empirical performances have been reported. However, the crucial model selection properties for hierarchical nonlocal priors in high-dimensional generalized linear regression have rarely been investigated. In this paper, we consider a hierarchical nonlocal prior for high-dimensional logistic regression models and investigate theoretical properties of the posterior distribution. Specifically, a product moment (pMOM) nonlocal prior is imposed over the regression coefficients with an Inverse-Gamma prior on the tuning parameter. Under standard regularity assumptions, we establish strong model selection consistency in a high-dimensional setting, where the number of covariates is allowed to increase at a sub-exponential rate with the sample size. We implement the Laplace approximation for computing the posterior probabilities, and a modified shotgun stochastic search procedure is suggested for efficiently exploring the model space. We demonstrate the validity of the proposed method through simulation studies and an RNA-sequencing dataset for stratifying disease risk.
