论文标题
回归模型中使用正常化合物伽玛先验的统计推断
Statistical inference with normal-compound gamma priors in regression models
论文作者
论文摘要
缩放混合收缩率最近已显示出具有强大的经验性能和出色的理论特性，例如模型选择一致性和（接近）最小值后的收缩率。在本文中，由于对具有伽马分布的相应反向尺度参数的复合而产生的正常化合物γ先验（NCG）被用作比例参数的先验。由于其与各种有用模型的关系，该模型的吸引力变得显而易见。高参数的调整给出了其他一些模型所表现出的相同收缩特性。使用不同的条件，后验既一致，并且根据一组假设的集合，既具有强烈的一致性，并且具有几乎最佳的收缩率。此外，得出了蒙特卡洛马尔可夫链（MCMC）和变异贝叶斯算法，然后提出了一种方法来更新超参数，并将其掺入MCMC和变异贝叶斯算法中。最后，使用真实数据和模拟数据证明了该模型吸引力的经验证据，以将预测结果与以前的模型进行比较。
Scale-mixture shrinkage priors have recently been shown to possess robust empirical performance and excellent theoretical properties such as model selection consistency and (near) minimax posterior contraction rates. In this paper, the normal-compound gamma prior (NCG) resulting from compounding on the respective inverse-scale parameters with gamma distribution is used as a prior for the scale parameter. Attractiveness of this model becomes apparent due to its relationship to various useful models. The tuning of the hyperparameters gives the same shrinkage properties exhibited by some other models. Using different sets of conditions, the posterior is shown to be both strongly consistent and have nearly-optimal contraction rates depending on the set of assumptions. Furthermore, the Monte Carlo Markov Chain (MCMC) and Variational Bayes algorithms are derived, then a method is proposed for updating the hyperparameters and is incorporated into the MCMC and Variational Bayes algorithms. Finally, empirical evidence of the attractiveness of this model is demonstrated using both real and simulated data, to compare the predicted results with previous models.
