Bayesian variable selection methods are powerful techniques for fitting and inferring on sparse high-dimensional linear regression models. However, many are computationally intensive or require restrictive prior distributions on model parameters. Likelihood based penalization methods are more computationally friendly, but resource intensive refitting techniques are needed for inference. In this paper, we proposed an efficient and powerful Bayesian approach for sparse high-dimensional linear regression. Minimal prior assumptions on the parameters are required through the use of plug-in empirical Bayes estimates of hyperparameters. Efficient maximum a posteriori probability (MAP) estimation is completed through the use of a partitioned and extended expectation conditional maximization (ECM) algorithm. The result is a PaRtitiOned empirical Bayes Ecm (PROBE) algorithm applied to sparse high-dimensional linear regression. We propose methods to estimate credible and prediction intervals for predictions of future values. We compare the empirical properties of predictions and our predictive inference to comparable approaches with numerous simulation studies and an analysis of cancer cell lines drug response study. The proposed approach is implemented in the R package probe.

翻译：Bayesian变量选择方法是对稀有的高维线性回归模型进行安装和推断的有力技术,但许多是计算密集的,或需要事先对模型参数进行限制性分配。以可能性为基础的惩罚方法在计算上较为友好,但需要资源密集的调整方法来推断。在本文中,我们提出了一种高效和强大的Bayesian方法,用于稀有的高维线性线性回归。需要通过使用超光谱的插座实验性Bayes估计数,对这些参数作出最起码的先前假设。通过使用分离和扩展的预期有条件最大化(ECM)算法,完成了后继概率(MAP)的有效估计。结果是一种PARtitiooned实验性Bayes Ecm(PROBE)算法,用于稀少高维度线性线性线性回归。我们提出了估算未来值预测的可靠和预测间隔的方法。我们用大量模拟研究和分析癌症细胞反应系列研究来比较预测和预测的预测性推论与可比较的方法。拟议的方法在Ragage 探测器中实施。