A note on noninformative priors for Weibull distributions
A note on noninformative priors for Weibull distributions
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DOI：
10.1016/s0378-3758(96)00155-3
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发表时间：
1997-06-16
影响因子：
0.9
通讯作者：
Sun, D
中科院分区：
文献类型：
--
作者：
Sun, D
本文研究了两参数威布尔分布的无信息先验。对于威布尔模型之一，Berger和Bernardo的（J. Amer. Statistist. Assoc.84（1989），200-207;在：Bayesian Statistics（1992），Oxford Univ. Press，Oxford，35-60中），前向和后向参考先验被示出为是相同的，但不同于Jeffreys先验。一般形式的二阶匹配先验的推导，当一个或两个参数的兴趣。Jeffreys先验不是二阶匹配先验，但参考先验总是三阶匹配先验。此外，当两个参数都感兴趣时，参考先验是唯一的二阶匹配先验。基于Jeffreys和参考先验的小样本后验置信集的频率覆盖概率进行了比较。对于小样本量，参考先验也优于Jeffreys先验上级。它也说明了一个滋扰参数的选择是非常重要的。
In this note, noninformative priors for two-parameter Weibull distributions are investigated. For one of the Weibull models, Berger and Bernardo's (J. Amer. Statist. Assoc. 84 (1989), 200-207; In: Bayesian Statistics (1992), Oxford Univ. Press, Oxford, 35-60) forward and backward reference priors are shown to be the same, but differ from the Jeffreys prior. General forms of the second-order matching priors are derived, when one or both parameters are of interest. The Jeffreys prior is not a second-order matching prior, but the reference prior is a always a third-order matching prior. Furthermore, when both parameters are of interest, the reference prior is the unique second-order matching prior. Frequentist coverage probabilities of the small sample posterior confidence sets based on the Jeffreys and reference priors are compared. The reference prior is also superior to the Jeffreys prior for small sample sizes. It is also illustrated that the choice of a nuisance parameter is very important.