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

• Project/Area Number: 17500178
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Statistical science
• Research Institution: The University of Tokyo
• Principal Investigator: KOMAKI Fumiyasu The University of Tokyo, Graduate School of Information Science and Technology, Associate Professor (70242039)
• Project Period (FY): 2005 – 2007
• Project Status: Completed (Fiscal Year 2007)
• Budget Amount: ¥3,830,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥330,000); Fiscal Year 2007: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2006: ¥1,100,000 (Direct Cost: ¥1,100,000); Fiscal Year 2005: ¥1,300,000 (Direct Cost: ¥1,300,000)
• Keywords: Bayesian theory / prediction / information geometry / ポアソンモデル / 漸近理論 / 決定理論

Research Abstract

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.

Research Products

• [Journal Article] Information geometry of small diffusions (2008)
  • Author(s): Sei, T., and Komaki, F
  • Journal Title: Statistical Inference for Stochastic Processes (In press)(掲載確定)(In press)
  • Description: 「研究成果報告書概要(和文)」より
  • Peer Reviewed
• [Journal Article] The information geometric structure of generalized empirical like lihood estimators (2008)
  • Author(s): Nishimura, T. and Komaki, F
  • Journal Title: Communications in Statistics-Theory and Methods 37 Pages: 1867-1879
  • Description: 「研究成果報告書概要(和文)」より
  • Peer Reviewed
• [Journal Article] A superharmonic prior for the autoregressive process of the second order (2008)
  • Author(s): Tanaka, F. and Komaki, F
  • Journal Title: Journal of Time Series Analysis 29 Pages: 444-452
  • Description: 「研究成果報告書概要(和文)」より
  • Peer Reviewed
• [Journal Article] Bayesian shrikage prediction for the regression problem (2008)
  • Author(s): Kobayashi, K., and Komaki, F
  • Journal Title: Journal of Multivariate Analysis (In press)(掲載確定)(In press)
  • Description: 「研究成果報告書概要(和文)」より
  • Peer Reviewed
• [Journal Article] Information geometry of small diffusions (2008)
  • Author(s): Sei, T., and Komaki, F.
  • Journal Title: Statistical Inference for Stochastic Processes (in press)
  • Description: 「研究成果報告書概要(欧文)」より
• [Journal Article] The information geometric structure of generalized empirical likelihood estimators (2008)
  • Author(s): Nishimura, T. and Komaki, F.
  • Journal Title: Communications in Statistics -Theory and Methods vol. 37 Pages: 1867-1879
  • Description: 「研究成果報告書概要(欧文)」より
• [Journal Article] A superharmonic prior for the autoregressive process of the second order (2008)
  • Author(s): Tanaka, F. and Komaki, F.
  • Journal Title: Journal of Time. Series Analysis vol. 29 Pages: 444-452
  • Description: 「研究成果報告書概要(欧文)」より
• [Journal Article] Bayesian shrinkage prediction for the regression problem (2008)
  • Author(s): Kobayashi, K., and Komaki, F.
  • Journal Title: Journal of Multivariate Analysis (in press)
  • Description: 「研究成果報告書概要(欧文)」より
• [Journal Article] The information geometric structure of generalized empirical likelihood estimators (2008)
  • Author(s): Nishimura, T. and Komaki, F.
  • Journal Title: Communications in Statistics-Theory and Methods 37 Pages: 1867-1879
  • Peer Reviewed
• [Journal Article] Bayesian prediction and model selection for locally asymptotically mixed normal models (2007)
  • Author(s): Sei, T., and Komaki, F
  • Journal Title: Journal of Statistical Planning and Inference 137 Pages: 2523-2534
  • Description: 「研究成果報告書概要(和文)」より
  • Peer Reviewed
• [Journal Article] Bayesian prediction based on a class of shrinkage priors for location-scale models (2007)
  • Author(s): Komaki, F
  • Journal Title: Annals of the Institute of Statistical Mathematics 59 Pages: 135-146
  • Description: 「研究成果報告書概要(和文)」より
  • Peer Reviewed
• [Journal Article] Bayesian prediction and model selection for locally asymptotically mixed normal models (2007)
  • Author(s): Sei, T., and Komaki, F.
  • Journal Title: Journal of Statistical Planning and Inference vol. 137 Pages: 2523-2534
  • Description: 「研究成果報告書概要(欧文)」より
• [Journal Article] Bayesian prediction based on a class of shrinkage priors for location-scale models (2007)
  • Author(s): Komaki, F.
  • Journal Title: Annals of the Institute of Statistical Mathematics vol. 59 Pages: 135-146
  • Description: 「研究成果報告書概要(欧文)」より
• [Journal Article] Information geometry of small diffusions (2007)
  • Author(s): Sei, T., and komaki, F.
  • Journal Title: Statistical Inference for Stochastic Processes Online First(印刷中掲載確定)
  • Peer Reviewed
• [Journal Article] Bayesian prediction based on a class of shrinkage priors for location-scale models (2007)
  • Author(s): Komaki, R.
  • Journal Title: Annals of the Institute of Statistical Mathematics 59 Pages: 135-146
• [Journal Article] Bayesian prediction and model selection for locally asymptotically mixed normal models (2007)
  • Author(s): Sei, T., Komaki, F.
  • Journal Title: Journal of Statistical Planning and Inference 137 Pages: 2523-2534
• [Journal Article] Shrinkage priors for Bayesian prediction (2006)
  • Author(s): Komaki, F
  • Journal Title: the Annals of Statitics 34 Pages: 808-819
  • Description: 「研究成果報告書概要(和文)」より
  • Peer Reviewed
• [Journal Article] A class of proper priors for Bayesian simultaneous prediction of independent Poisson observables (2006)
  • Author(s): Komaki, F
  • Journal Title: Journal of Multivariate Analysis 97 Pages: 1815-1828
  • Description: 「研究成果報告書概要(和文)」より
  • Peer Reviewed
• [Journal Article] Information criteria for kernel machines (2006)
  • Author(s): Kobayashi, K., and Komaki, F
  • Journal Title: IEEE Transactions on Neural Neworks 17 Pages: 571-577
  • Description: 「研究成果報告書概要(和文)」より
  • Peer Reviewed
• [Journal Article] Shrinkage priors for Bayesian prediction (2006)
  • Author(s): Komaki, F.
  • Journal Title: the Annals of Statistics vol. 34 Pages: 808-819
  • Description: 「研究成果報告書概要(欧文)」より
• [Journal Article] A class of proper priors for Bayesian simultaneous prediction of independent Poisson observables (2006)
  • Author(s): Komaki, F.
  • Journal Title: Journal of Multivariate Analysis vol. 97 Pages: 1815-1828
  • Description: 「研究成果報告書概要(欧文)」より
• [Journal Article] Information criteria for kernel machines (2006)
  • Author(s): Kobayashi, K., and Komaki, F.
  • Journal Title: IEEE Transactions on Neural Networks vol. 17 Pages: 571-577
  • Description: 「研究成果報告書概要(欧文)」より
• [Journal Article] Shrinkage priors for Bayesian prediction (2006)
  • Author(s): Komaki, F.
  • Journal Title: the Annals of Statistics (印刷中)
• [Journal Article] A class of proper priors for Bayesian simultaneous prediction of independent Poisson observables (2006)
  • Author(s): Komaki, F.
  • Journal Title: Journal of Multivariate Analysis (印刷中)
• [Journal Article] Information criteria for kernel machines (2006)
  • Author(s): Kobayashi, K., Komaki, F.
  • Journal Title: IEEE Trans. on Neural Networks (印刷中)
• [Presentation] Bayesian adaptive design for binary response clinical trials (2007)
  • Author(s): Komaki, F and Biswas, A.
  • Organizer: First International Workshop in Sequential Methodologies
  • Place of Presentation: Auburn大学,米国
  • Year and Date: 2007-07-25
• [Presentation] Bayesian prediction based on shrinkage priors for the Neyman-Scott model (2007)
  • Author(s): Komaki, F
  • Organizer: International Conference on Statistical Science, OR&IT
  • Place of Presentation: Hotel Bliss, Tilpati, India
  • Description: 「研究成果報告書概要(和文)」より
• [Presentation] Bayesian adaptive design for binary response clinical trials (2007)
  • Author(s): Komaki, F. and Biswas, A
  • Organizer: First International Workshop in Sequential Methodologies
  • Place of Presentation: Auburn University, Auburn, U. S. A.
  • Description: 「研究成果報告書概要(和文)」より
• [Presentation] Bayesian prediction based on shrinkage priors for the Neyman-Scott model (2007)
  • Author(s): Komaki, F.
  • Organizer: International Conference on Statistical Science, OR & IT
  • Place of Presentation: Hotel Bliss, Tilpati, India.
  • Description: 「研究成果報告書概要(欧文)」より
• [Presentation] Information geometry of Bayesian inference (2005)
  • Author(s): Komaki, F
  • Organizer: The Second International Symposium on Information Geometry and Its Applications
  • Place of Presentation: University of Tokyo, Tokyo, Japan
  • Description: 「研究成果報告書概要(和文)」より
• [Presentation] Shrinkage prediction for the Normal regression problem with Kullback-Leibler loss function (2005)
  • Author(s): Kobayashi, K. and Komaki, F
  • Organizer: The Second International Symposium on Information Geometry and Its Applications
  • Place of Presentation: University of Tokyo,Tokyo, Japan
  • Description: 「研究成果報告書概要(和文)」より
• [Presentation] Geometrical structure of the ARMA model manifold and its application to Bayesian methods (2005)
  • Author(s): Tanaka, F. and Komaki, F
  • Organizer: The Second International Symposium on Information Geometry and Its Applications
  • Place of Presentation: University of Tokyo, Tokyo, Japan
  • Description: 「研究成果報告書概要(和文)」より
• [Presentation] Evaluation of the sign of the sectional curvature of the AR model manifold and construction of predictive distributions (2005)
  • Author(s): Tanaka, F. and Komaki, F
  • Organizer: STATDEP 2005
  • Place of Presentation: Paris, France
  • Description: 「研究成果報告書概要(和文)」より
• [Presentation] Risk sensitive decision networks. (2005)
  • Author(s): Kobayashi, K. and Komaki, F
  • Organizer: Second Latin American Congress on Bayesian Statistics
  • Place of Presentation: San Jose'del Cabo, Baja California, Mexico
  • Description: 「研究成果報告書概要(和文)」より
• [Presentation] Shrinkage prediction for the Normal regression problem with Kullback-Leibler loss function (2005)
  • Author(s): Kobayashi, K. and Komaki, F.
  • Organizer: The Second International Symposium on Information Geometry and Its Applications
  • Place of Presentation: University of Tokyo, Tokyo, Japan
  • Description: 「研究成果報告書概要(欧文)」より
• [Presentation] Geometrical structure of the ARAM model manifold and its application to Bayesian methods (2005)
  • Author(s): Tanaka, F. and Komaki, F.
  • Organizer: The Second International Symposium on Information Geometry and Its Applications
  • Place of Presentation: University of Tokyo, Tokyo, Japan
  • Description: 「研究成果報告書概要(欧文)」より
• [Presentation] Evaluation of the sign of the sectional curvature of the AR model manifold and construction of predictive distributions (2005)
  • Author(s): Tanaka, F. and Komaki, F.
  • Organizer: STATDEP 2005, Statistics for Dependent Data 2005
  • Place of Presentation: Paris, France.
  • Description: 「研究成果報告書概要(欧文)」より
• [Presentation] Risk sensitive decision networks (2005)
  • Author(s): Kobayashi, K. and Komaki, F.
  • Organizer: Second Latin American Congress on Bayesian Statistics
  • Place of Presentation: San Jose' del Cabo, Baja California, Mexico.
  • Description: 「研究成果報告書概要(欧文)」より