An analytical approach to Bayesian generalized linear models

• Project/Area Number: 20700259
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Statistical science
• Research Institution: The Institute of Statistical Mathematics
• Principal Investigator: OHNISHI Toshio The Institute of Statistical Mathematics, 大学院・経済学研究院, 准教授 (60353413)
• Project Period (FY): 2008 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000); Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2009: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000); Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: 統計数学 / 一般化線形モデル / Bayes統計学 / 共役事前分布 / Tweedie分布 / 降水量データ / 国際情報交換 / オーストラリア / 国際研究者交流 / Bayes統計

Research Abstract

The following three major topics were investigated.
(1) Noting the equality satisfied by the optimal predictive density, we discussed a Bayesian model selection criterion.
(2) We derived duality in the Bayesian estimation from the analytical property of having a conjugate prior.
(3) We investigated a linear mixed model that is based on a location family having a conjugate prior.
As an application study we analyzed the rainfall data of East Australia using a generalized linear model whose underlying distribution is the Tweedie distribution.

Research Products

• [Journal Article] Saddlepoint condition on a predictor to reconfirm the need for the assumption of a prior distribution (2011)
  • Author(s): Takemi Yanagimoto, Toshio Ohnishi
  • Journal Title: Journal of Statistical Planning and Inference 141
  • Peer Reviewed
• [Journal Article] Saddlepoint condition on a predictor to reconfirm the need for the assumption of a prior distribution (2011)
  • Author(s): Takemi Yanagimoto
  • Journal Title: Journal of Statistical Planning and Inference Volume: 141 Pages: 1990-2000
  • Peer Reviewed
• [Journal Article] Duality induced from conjugacy in the curved exponential family (2010)
  • Author(s): Toshio Ohnishi, Takemi Yanagimoto
  • Journal Title: Journal of the Japan Statistical Society 40 Pages: 23-43
  • NAID: 10026983516
  • URL: http://www.terrapub.co.jp/journals/jjss/abstract/4001/40010023.html
  • Peer Reviewed
• [Journal Article] Duality induced from conjugacy in the curved exponential family (2010)
  • Author(s): Toshio Ohnishi
  • Journal Title: Journal of the Japan Statistical Society Volume: 40 Pages: 23-43
  • NAID: 10026983516
  • Peer Reviewed
• [Journal Article] Predictive credible region for Bayesian diagnosis of a hypothesis (2009)
  • Author(s): Takemi Yanagimoto, Toshio Ohnishi
  • Journal Title: Journal of the Japan Statistical Society 39 Pages: 111-131
  • NAID: 10025991948
  • URL: http://www.terrapub.co.jp/journals/jjss/pdf/3901/39010111.pdf
  • Peer Reviewed
• [Journal Article] Bayesian prediction of a density function in terms of e-mixture (2009)
  • Author(s): Takemi Yanagimoto, Toshio Ohnishi
  • Journal Title: Journal of Statistical Planning and Inference 139
  • Peer Reviewed
• [Journal Article] Tweedie一般化線形モデルを用いたクイーンズランド州の降水量データの解析 (2009)
  • Author(s): 大西俊郎, Peter Dunn
  • Journal Title: 京都大学数理解析研究所講究録 1621 Pages: 135-152
  • URL: http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/1621-10.pdf
  • Peer Reviewed
• [Journal Article] Tweedie一般化線形モデルを用いたクイーンズランド州の降水量データの解析 (2009)
  • Author(s): 大西俊郎・Peter Dunn
  • Journal Title: 京都大学数理解析研究所講究録 1621 Pages: 135-152
• [Journal Article] Bayesian Prediction of a Density Function in Terms of e-Mixture (2009)
  • Author(s): Takemi Yanagimoto and Toshio Ohnishi
  • Journal Title: Journal of Statistical Planning and Inference (In press)
  • Peer Reviewed
• [Journal Article] Predictive credible region for Bayesian diagnosis of a hypothesis (2009)
  • Author(s): Takemi Yanagimoto and Toshio Ohnishi
  • Journal Title: Journal of the Japan Statistical Society (Accepted)
  • NAID: 10025991948
  • Peer Reviewed
• [Presentation] Saddlepoint condition on a predictor and its implication (2011)
  • Author(s): 大西俊郎, 柳本武美
  • Organizer: RIMS共同研究"Statistical Information in Inference and Its Related Topics"
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2011-03-08
• [Presentation] Saddlepoint condition on a predictor and its implication (2011)
  • Author(s): 大西俊郎
  • Organizer: RIMS共同研究"Statistical Information in Inference and Its Related Topics"
  • Place of Presentation: 京都大学 数理解析研究所
  • Year and Date: 2011-03-08
• [Presentation] 計算機支援による統計手法,理論・応用およびその周辺 (2010)
  • Author(s): 柳本武美, 大西俊郎
  • Organizer: 事後密度にのみ基づいた経験Bayes法の利点科研費研究集会
  • Place of Presentation: 高知大学
  • Year and Date: 2010-11-26
• [Presentation] 事後密度にのみ基づいた経験Bayes法の利点 (2010)
  • Author(s): 柳本武美
  • Organizer: 科研費研究集会「計算機支援による統計手法、理論・応用およびその周辺」
  • Place of Presentation: 高知大学
  • Year and Date: 2010-11-26
• [Presentation] 計算代数手法に基づく数理統計学の展開 (2010)
  • Author(s): 大西俊郎, 柳本武美
  • Organizer: Location family における鞍点等式とその含意科研費研究集会
  • Place of Presentation: 大宮ソニックシティー
  • Year and Date: 2010-11-16
• [Presentation] Location familyにおける鞍点等式とその含意 (2010)
  • Author(s): 大西俊郎
  • Organizer: 科研費研究集会「計算代数手法に基づく数理統計学の展開」
  • Place of Presentation: 大宮ソニックシティー
  • Year and Date: 2010-11-16
• [Presentation] 事前分布の仮定を促進する経験Bayes法の展開 (2010)
  • Author(s): 柳本武美, 大西俊郎
  • Organizer: 統計関連学会連合大会
  • Place of Presentation: 早稲田大学
  • Year and Date: 2010-09-07
• [Presentation] Location familyにおける鞍点等式とその含意 (2010)
  • Author(s): 大西俊郎, 柳本武美
  • Organizer: 統計関連学会連合大会
  • Place of Presentation: 早稲田大学
  • Year and Date: 2010-09-07
• [Presentation] 水産資源に対する観察データ解析のための統計推測 e-混合型予測分布によるBayes予測およびそのモデル選択への応用 (2010)
  • Author(s): 大西俊郎
  • Organizer: 統計数理研究所共同利用研究集会
  • Place of Presentation: 統計数理研究所
  • Year and Date: 2010-03-09
• [Presentation] e-混合型予測分布による Bayes 予測およびそのモデル選択への応用 (2010)
  • Author(s): 大西俊郎
  • Organizer: 統計数理研究所 共同利用研究集会「水産資源に対する観察データ解析のための統計推測」
  • Place of Presentation: 統計数理研究所(東京都)
  • Year and Date: 2010-03-09
• [Presentation] Bayesian prediction in terms of e-mixture and its implication Institute of Statistical Mathematics, Indian Statistical Institute and Institute of Statistical Science (2010)
  • Author(s): Toshio Ohnishi
  • Organizer: Academia Sinica Joint Meeting
  • Place of Presentation: Indian Statistical Institute, Kolkata, India.
  • Year and Date: 2010-01-22
• [Presentation] Bayesian prediction in terms of e-mixture and its implication (2010)
  • Author(s): 大西俊郎
  • Organizer: Institute of Statistical Mathematics, Indian Statistical Institute and Institute of Statistical Science, Academia Sinica Joint Meeting
  • Place of Presentation: Indian Statistical Institute(Kolkata, India)
  • Year and Date: 2010-01-22
• [Presentation] 統計科学の数理と応用 (2009)
  • Author(s): 大西俊郎, Peter Dunn
  • Organizer: Conjugate analysis of a linear mixed model in the location family科研費研究集会
  • Place of Presentation: 岡山国際交流センター
  • Year and Date: 2009-10-07
• [Presentation] Conjugate analysis of a linear mixed model in the location family (2009)
  • Author(s): 大西俊郎, Peter Dunn
  • Organizer: 科研費研究集会「統計科学の数理と応用」
  • Place of Presentation: 岡山国際交流センター(岡山県)
  • Year and Date: 2009-10-07
• [Presentation] Conjugate analysis of a generalized linear mixed model (2009)
  • Author(s): 大西俊郎, Peter Dunn
  • Organizer: 統計関連学会連合大会
  • Place of Presentation: 同志社大学
  • Year and Date: 2009-09-08
• [Presentation] Conjugate analysis of a generalized linear mixed model (2009)
  • Author(s): 大西俊郎, Peter Dunn
  • Organizer: 統計関連学会連合大会
  • Place of Presentation: 同志社大学(京都府)
  • Year and Date: 2009-09-08
• [Presentation] 水産資源に対する観察データ解析のための統計推測 (2008)
  • Author(s): 大西俊郎
  • Organizer: Tweedie一般化線形モデルのBayes解析統計数理研究所共同利用研究
  • Place of Presentation: 統計数理研究所
  • Year and Date: 2008-09-25
• [Presentation] Tweedie一般化線形モデルのBayes解析 (2008)
  • Author(s): 大西俊郎
  • Organizer: 統計数理研究所共同利用研究「水産資源に対する観察データ解析のための統計推測」
  • Place of Presentation: 統計数理研究所(東京)
  • Year and Date: 2008-09-25
• [Presentation] Bayesian最適予測子を用いた仮説の診断法の提案 (2008)
  • Author(s): 大西俊郎, 柳本武美
  • Organizer: 統計関連学会連合大会
  • Place of Presentation: 慶應義塾大学
  • Year and Date: 2008-09-10
• [Presentation] Bayesian最適予測子を用いた仮説の診断法の提案 (2008)
  • Author(s): 大西俊郎・柳本武美
  • Organizer: 2008年度統計関連学会連合大会
  • Place of Presentation: 慶應義塾大学(神奈川)
  • Year and Date: 2008-09-10