A theoretical approach to Bayesian statistical inference by a special shrinkage prior distribution

通过特殊收缩先验分布进行贝叶斯统计推断的理论方法

• 批准号: 21740065
• 负责人: MARUYAMA Yuzo
• 金额: $ 2.83万
• 依托单位: The University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21740065/
• 关键词: 数理統計学; 統計科学; 統計数学; ベイズ理論

For the balanced ANOVA setup, we propose a new closed form Bayes factor without integral representation, which is however based on fully Bayes method, with reasonable model selection consistency for two asymptotic situations (either number of levels of the factor or number of replication in each level goes to infinity). Exact analytical calculation of the marginal density under a special choice of the priors enables such a Bayes factor. The most advantage of our Bayes factor over existing Bayes factors is its excellent closed form. Since many Bayes factors based on fully Bayes method involve the integral in the representation, they have to apply the Laplace approximation in practice. However, the answer to the question which type of the Laplace approximation is more appropriate, is obscure for some cases. On the other hand, our Bayes factor does not require thought and has a reasonable model selection consistency

对于平衡方差分析设置，我们提出了一种新的不带积分表示的封闭形式贝叶斯因子，该因子基于完全贝叶斯方法，对于两种渐近情况（因子的水平数或每一水平上的复制数趋于无穷大）具有合理的模型选择一致性。在一种特殊的先验选择下，精确的边际密度解析计算使这种贝叶斯因子成为可能。与现有的贝叶斯因子相比，我们的贝叶斯因子最大的优点是它具有良好的封闭形式。由于许多基于全贝叶斯方法的贝叶斯因子在表示中涉及到积分，在实际应用中不得不采用拉普拉斯近似。然而，在某些情况下，哪种类型的拉普拉斯近似更合适这个问题的答案是模糊的。另一方面，我们的贝叶斯因子不需要思考，具有合理的模型选择一致性

项目成果

Improved robust Bayes estimators of the error variance in linear models.

改进了线性模型中误差方差的稳健贝叶斯估计器。

• 发表时间: 2013
• 期刊: Journal of Statistical Planning and Inference
• 影响因子: 0.9
• 作者: K. Osanai;M. Inoue;岡本 創;肥後祐司;Jun Akimitsu;Yuzo Maruyama and William E. Strawderman
• 通讯作者: Yuzo Maruyama and William E. Strawderman

(Poster Presentataion) Bayesian variable selection with sub-harmonic priors.

（海报演示）具有次谐波先验的贝叶斯变量选择。

• 发表时间: 2010

An extended class of minimax generalized Bayes estimators of regression coefficients

回归系数的极小极大广义贝叶斯估计量的扩展类

• 发表时间: 2010
• 期刊: Journal of Multivariate Analysis
• 影响因子: 1.6
• 作者: Yuzo Maruyama;William Strawderman
• 通讯作者: William Strawderman

Bayesian predictive densities for linear regression models under alpha-divergence loss : some results and open problems

α散度损失下线性回归模型的贝叶斯预测密度：一些结果和开放问题

• DOI: 10.1214/11-imscoll803
• 发表时间: 2012
• 期刊: IMS Collections
• 作者: Edward;I. George and Yuzo Maruyama;Yasufumi Nitta and Ken'ichi Sekiya;Yuzo Maruyama and William E. Strawderman;新田 泰文;Yasufumi Nitta;Yuzo Maruyama and William E. Strawderman
• 通讯作者: Yuzo Maruyama and William E. Strawderman

Fully Bayes Model Selection with a Generalized g-Prior.

具有广义 g 先验的完全贝叶斯模型选择。

• 发表时间: 2010