CONSISTENCY OF BAYESIAN PROCEDURES FOR VARIABLE SELECTION
CONSISTENCY OF BAYESIAN PROCEDURES FOR VARIABLE SELECTION
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DOI：
10.1214/08-aos606
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发表时间：
2009-06-01
影响因子：
4.5
通讯作者：
Moreno, Elias
中科院分区：
文献类型：
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作者：
Casella, George;Giron, F. Javier;Moreno, Elias
人们早就知道，对于两两嵌套模型的比较，基于贝叶斯因子的决策产生1一致的模型选择器（在频率论意义上）。在这里，我们超越了嵌套成对模型通常的一致性，并表明，对于广泛的先验分布，包括内在先验，正态回归中相应的变量选择贝叶斯过程在整个正态线性模型中是一致的。我们发现贝叶斯因子的渐近性与Schwarz （BIC）准则的渐近性相等。此外，回想一下Jeffreys-Lindley悖论指的是一个众所周知的事实，即当共轭先验的方差趋于无穷时，对正态平均参数的点零假设总是被接受的。这意味着适当先验分布的某些极限形式不一定适用于测试问题。固有先验是适当先验分布的极限，对于有限的样本量，它们已被证明对回归中的变量选择表现得非常好；，我们的结果的结论是，对于内在先验，林德利悖论不会出现。
It has long been known that for the comparison of pairwise nested models, a decision based on the Bayes factor produces I consistent model selector (in the frequentist sense). Here we go beyond the usual consistency for nested pairwise models, and show that for a wide class of prior distributions, including intrinsic priors, the corresponding Bayesian procedure for variable selection in normal regression is consistent in the entire class of normal linear models. We find that the asymptotics of the Bayes factors for intrinsic priors are equivalent to those of the Schwarz (BIC) criterion. Also, recall that the Jeffreys-Lindley paradox refers to the well-known fact that a point null hypothesis on the normal mean parameter is always accepted when the variance of the conjugate prior goes to infinity. This implies that some limiting forms of proper prior distributions are not necessarily Suitable for testing problems. Intrinsic priors are limits of proper prior distributions, and for finite sample sizes they have been proved to behave extremely well for variable selection in regression;,I consequence of our results is that for intrinsic priors Lindley's paradox does not arise.