Permissible boundary prior function as a virtually proper prior density
Permissible boundary prior function as a virtually proper prior density
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允许边界先验函数作为实际上适当的先验密度
DOI：
10.1007/s10463-013-0421-1
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发表时间：
2014
影响因子：
1
通讯作者：
Toshio Ohnishi
中科院分区：
文献类型：
--
作者：
Takemi Yanagimoto;Toshio Ohnishi
提出了一个不适当的先验函数被视为一个实际上正确的先验密度的正则性条件，并讨论了它们的含义。这两个正则性条件要求先验函数被定义为适当的先验密度序列的极限，并且诱导后验密度被导出为相应的后验密度序列的光滑极限。将这种方法与经验贝叶斯方法中熟悉的未知点处退化先验密度的假设进行比较。比较研究也延伸到一个不适当的先验函数的假设，讨论单独从任何适当的先验密度。属性和例子索赔潜在的有用性所提出的概念。
Regularity conditions for an improper prior function to be regarded as a virtually proper prior density are proposed, and their implications are discussed. The two regularity conditions require that a prior function is defined as a limit of a sequence of proper prior densities and also that the induced posterior density is derived as a smooth limit of the sequence of corresponding posterior densities. This approach is compared with the assumption of a degenerated prior density at an unknown point, which is familiar in the empirical Bayes method. The comparison study extends also to the assumption of an improper prior function discussed separately from any proper prior density. Properties and examples are presented to claim potential usefulness of the proposed notion.