Frequentist validity of posterior quantiles for a two-parameter exponential family
Frequentist validity of posterior quantiles for a two-parameter exponential family
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DOI：
10.1093/biomet/83.1.55
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发表时间：
1996-03
期刊：
影响因子：
2.7
通讯作者：
Dongchu Sun;K. Ye
中科院分区：
文献类型：
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作者：
Dongchu Sun;K. Ye
Berger & Bernardo（1989）的参考先验和Tibshirani（1989）的先验是针对Bar-Lev &雷泽（1982）的双参数指数族中的分布导出的，当位置或尺度参数是感兴趣的时。参考先验被示出为Tibshirani先验。此外，条件下，Tibshirani先验是高阶匹配先验进行了研究。当这两个参数都感兴趣时，它也表明，参考先验与先验匹配的后验和频率论的扩展的对数似然比的基础上的有符号的平方根。正态分布、逆高斯分布和伽马分布被用来说明结果。
SUMMARY Berger & Bernardo's (1989) reference priors and Tibshirani (1989) priors are derived for distributions in Bar-Lev & Reiser's (1982) two-parameter exponential family when either the location or the scale parameter is of interest. The reference prior is shown to be a Tibshirani prior. Furthermore, conditions under which a Tibshirani prior is a higherorder matching prior are investigated. When both the parameters are of interest, it is also shown that the reference prior agrees with the prior matching the posterior and frequentist expansions based on the signed square root of log-likelihood ratio. The normal, inverse Gaussian, and gamma distributions are used to illustrate the results.