Bayes tests for linearly constrained parameters

线性约束参数的贝叶斯测试

• 批准号: 11680329
• 负责人: SUGIURA Nariaki
• 金额: $ 1.09万
• 依托单位: Japan Women's University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11680329/
• 关键词: Loop-ordered alternatives; Simple ordered alternatives; Tree ordered alternatives; Polyhedral convex cone; likelihood ratio test; minimax contrast test; Half-normal prior; Change point model; Simulation; Linear regression with unequal variances /

Generalized Bayes test for loop-ordered normal means is derived and it is shown that the minimum power of the test is almost the same as that of the likelihood ratio test but that the maximum power is fairly larger than the likelihood ratio test. The polyhedral convex cone formed by the loop-ordered alternatives has a set of pairs of two corner vectors which are most distant from the center, intersecting with the central vector of the cone with the equal angle. It is shown that uniform prior should be taken on the corner vectors located most far from the center. The generalized Bayes test having the uniform prior on the most nearest corner vectors from the center has poor global power and is not recommended, though it seems intuitively appealing without geometrical consideration and has simple expression. The same consideration yields Bayes tests for simple ordered normal means and tree ordered normal means. Thegeneralized Bayes tests are also derived by taking the limit of half-normal priors.Bayes test for testing the homogeneity of variances before and after the change point in a normal linear regression model is derived. For noninformative prior, posterior distribution of the ratio of variances is derived and the confidence interval is constructed. It is shown that test based on confidence interval is superior to the usual test based on the maximum likelihood estimates in that it guarantees the type I error. The renal transplant data is analyzed by this Bayes test and is found that the variances before and after the operation do not change significantly.

推导了循环订购的正常均值的广义贝叶斯测试，并表明测试的最小功率几乎与似然比测试的最小功率相同，但最大功率大于可能性比测试。由环排序的替代方案形成的多面体凸锥具有一组两个角向量，它们与中心最远，与锥的中心向量与锥形相等的角度相交。结果表明，应在远离中心的角向量上进行统一的先验。在中心最接近的角向量上具有统一的先验的广义贝叶斯测试的全球功率较差，不建议使用，尽管在没有几何学考虑的情况下，它似乎具有直觉上的吸引力，并且具有简单的表达。相同的考虑会产生贝叶斯测试的简单有序的正常均值和树序的正常均值。贝叶斯测试也通过采取半正常先验的限制来得出。BAYES测试在得出正常线性回归模型中变化点之前和之后的方差均匀性。对于非信息先验，得出了方差比的后验分布，并构建了置信区间。结果表明，基于置信区间的测试基于最大似然估计值优于通常的测试，因为它可以保证I型错误。通过此贝叶斯测试对肾移植数据进行分析，发现操作前后的方差不会显着变化。

项目成果

N. Sugiura: "Generalized Bayes and multiple contrast tests for simple loop-ordered normal means"Communications in Statistics-Theory Meth.. 28(3&4). 549-580 (1999)

N. Sugiura：“简单循环有序正态均值的广义贝叶斯和多重对比检验”统计理论方法通讯.. 28(3

N.Sugiura and N.Tateaoka: "Homogeneity of variances in normal linear regressor with a change point"Commun, in Statorl-Theory Meth.. 28(12). 2785-2801 (1999)

N.Sugiura 和 N.Tateaoka：“具有变化点的正态线性回归量的方差同质性”Commun，在 Statorl-Theory Meth.. 28(12) 中。

Sugiura, N.and Takaoka, , N.: "Homogeneity of variances in normal linear regression with a change point."Commun.Statist.. 28. 2785-2801 (1999)

Sugiura, N. 和 Takaoka, , N.：“具有变化点的正态线性回归中方差的同质性。”Commun.Statist.. 28. 2785-2801 (1999)

N.Sugiura: "generalized Bayes and multiple contrast teats for simple loop-ordered normal means"Commun, in Statort.-Theory Meth.. 28(3&4). 549-590 (1999)

N.Sugiura：“用于简单循环排序正态平均值的广义贝叶斯和多重对比乳头”Commun，in Statort.-Theory Meth.. 28(3