新方法提升线性模型变量选择效率，自动区分参数重要性。
Dirichlet process mixtures of block $g$ priors for model selection and prediction in linear models
- 用分块g先验的狄利克雷过程混合建模，按数据自选参数块差异化收缩。
- 小样本中大效应下，检测微弱显著效应的效能更高，假阳性略增。
- 适合高维线性模型变量选择，尤其含少数强效应的场景。
本文提出狄利克雷过程混合分块g先验，用于线性模型的变量选择与预测。该方法扩展了传统g先验，允许对数据选定的参数块进行差异收缩，同时充分考虑预测变量的相关结构，连接了变量选择与连续收缩先验的研究脉络。我们证明该先验在多种意义下具有一致性，尤其避免了Som等（2016）指出的条件林德利悖论。此外，我们设计了一种马尔可夫链蒙特卡洛算法，仅需少量调参即可实现后验推断。在真实与模拟数据上的实证研究显示：当存在少量极大效应时，该先验能显著提升对较小但显著效应的检出能力，且假阳性数量增加极小。
原文摘要 · Abstract (English)
This paper introduces Dirichlet process mixtures of block $g$ priors for model selection and prediction in linear models. These priors are extensions of traditional mixtures of $g$ priors that allow for differential shrinkage for various (data-selected) blocks of parameters while fully accounting for the predictors' correlation structure, providing a bridge between the literatures on model selection and continuous shrinkage priors. We show that Dirichlet process mixtures of block $g$ priors are consistent in various senses and, in particular, that they avoid the conditional Lindley ``paradox'' highlighted by Som et al. (2016). Further, we develop a Markov chain Monte Carlo algorithm for posterior inference that requires only minimal ad-hoc tuning. Finally, we investigate the empirical performance of the prior in various real and simulated datasets. In the presence of a small number of very large effects, Dirichlet process mixtures of block $g$ priors lead to higher power for detecting smaller but significant effects without only a minimal increase in the number of false discoveries.
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