Compatibility of Prior Specifications Across Linear Models
Compatibility of Prior Specifications Across Linear Models
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DOI：
10.1214/08-sts258
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发表时间：
2008-08-01
影响因子：
5.7
通讯作者：
Veronese, Piero
中科院分区：
文献类型：
--
作者：
Consonni, Guido;Veronese, Piero
贝叶斯模型比较需要在每个候选模型的参数空间上指定先验分布。在这方面出现了两个问题：一方面，启发任务迅速成为禁止的模型数量的增加;另一方面，许多先前的规格只能加剧众所周知的敏感性事先转让，从而产生不太可靠的结论。在主观的框架内，这两个困难可以抵消连接先验跨模型，以实现简化和兼容性，我们讨论相关的客观方法的链接。给定一个包含的，或完整的，模型连同其参数空间上的先验，我们回顾和总结了一些程序，推导先验下的子模型，即边缘化，空调，Kullback-Leibler投影。这些技术进行了说明和讨论，参考变量选择线性模型采用传统的g-先验，与现有的标准方法进行比较。最后，通过模拟和真实的数据集，每个程序的相对优点进行了评估。
Bayesian model comparison requires the specification of a prior distribution on the parameter space of each candidate model. In this connection two concerns arise: on the one hand the elicitation task rapidly becomes prohibitive as the number of models increases; on the other hand numerous prior specifications can only exacerbate the well-known sensitivity to prior assignments, thus producing less dependable conclusions. Within the subjective framework, both difficulties can be counteracted by linking priors across models in order to achieve simplification and compatibility; we discuss links with related objective approaches. Given an encompassing, or full, model together with a prior on its parameter space, we review and summarize a few procedures for deriving priors under a submodel, namely marginalization, conditioning, and Kullback-Leibler projection. These techniques are illustrated and discussed with reference to variable selection in linear models adopting a conventional g-prior; comparisons with existing standard approaches are provided. Finally, the relative merits of each procedure are evaluated through simulated and real data sets.