The calculation of posterior distributions by data augmentation
The calculation of posterior distributions by data augmentation
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DOI：
10.1080/01621459.1987.10478458
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发表时间：
1987-06
影响因子：
3.7
通讯作者：
M. Tanner;W. Wong
中科院分区：
文献类型：
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作者：
M. Tanner;W. Wong
摘要数据扩充的思想在缺失值问题中自然产生，例如在平衡双向表中填充缺失单元格的标准方法。因此，数据扩充是指对观测数据进行扩充以使其更易于分析的方案。这个装置被EM算法（Dempster，Laird，and Rubin 1977）用于解决最大似然问题。在可能性不能用正态似然近似的情况下，不能依赖最大似然估计和相关的标准误差来做出有效的推断。从贝叶斯的角度来看，现在必须计算感兴趣的参数的后验分布。如果数据增强可以用于最大似然估计的计算，那么在相同的情况下，人们应该能够将其用于后验分布的计算。本文的目的是解释如何做到这一点。基本的想法是...
Abstract The idea of data augmentation arises naturally in missing value problems, as exemplified by the standard ways of filling in missing cells in balanced two-way tables. Thus data augmentation refers to a scheme of augmenting the observed data so as to make it more easy to analyze. This device is used to great advantage by the EM algorithm (Dempster, Laird, and Rubin 1977) in solving maximum likelihood problems. In situations when the likelihood cannot be approximated closely by the normal likelihood, maximum likelihood estimates and the associated standard errors cannot be relied upon to make valid inferential statements. From the Bayesian point of view, one must now calculate the posterior distribution of parameters of interest. If data augmentation can be used in the calculation of the maximum likelihood estimate, then in the same cases one ought to be able to use it in the computation of the posterior distribution. It is the purpose of this article to explain how this can be done. The basic idea ...