Information geometry and Bayesian inference for high-dimensional parametric and semi-parametric models

高维参数和半参数模型的信息几何和贝叶斯推理

• 批准号: 17500178
• 负责人: KOMAKI Fumiyasu
• 金额: $ 2.45万
• 依托单位: The University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2005
• 资助国家: 日本
• 起止时间: 2005 至 2007
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-17500178/
• 关键词: Bayesian theory; prediction; information geometry; ポアソンモデル; 漸近理論; 決定理論

Prediction and inference methods for high-dimensional models and semiparametric models have been investigated. It is shown that the model manifold of the Neyman-Scott model is the space with constant negative curvature. The Neyman-Scott model is formulated as a transformation group model. A predictive density dominating the best invariant predictive density has been constructed by using information geometry. Furthermore, empirical likelihood methods for semiparametric models have been studied. Empirical likelihood methods were formulated in the framework of information geometry.Prediction methods for statistical problems with multiplicity have also been studied.

研究了高维模型和半参数模型的预测和推理方法。证明了Neyman-Scott模型的模型流形是具有恒定负曲率的空间。Neyman-Scott模型被表述为一个转换群模型。利用信息几何构造了一个支配最佳不变预测密度的预测密度。此外，还研究了半参数模型的经验似然方法。在信息几何的框架下，提出了经验似然方法。对具有多重统计问题的预测方法也进行了研究。

项目成果

Risk sensitive decision networks.

风险敏感决策网络。

• 发表时间: 2005
• 作者: Kobayashi;K. and Komaki;F
• 通讯作者: F

Bayesian prediction based on shrinkage priors for the Neyman-Scott model

基于 Neyman-Scott 模型收缩先验的贝叶斯预测

• 发表时间: 2007
• 作者: Komaki;F
• 通讯作者: F

Bayesian shrikage prediction for the regression problem

回归问题的贝叶斯收缩预测

• 发表时间: 2008
• 期刊: Journal of Multivariate Analysis (In press)(掲載確定)(In press)
• 作者: Kobayashi;K.;and Komaki;F
• 通讯作者: F

Information Criteria for Kernel Machines

• 发表时间: 2005
• 作者: Kei Kobayashi;F. Komaki

Evaluation of the sign of the sectional curvature of the AR model manifold and construction of predictive distributions

AR模型流形截面曲率符号的评估和预测分布的构建

• 发表时间: 2005
• 作者: Tanaka;F. and Komaki;F
• 通讯作者: F