Reconstructing the empirical Bayes method through the use of the posterior density

• Project/Area Number: 23500357
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Statistical science
• Research Institution: Chuo University
• Principal Investigator: YANAGIMOTO Takemi 中央大学, 理工学部, その他 (40000195)
• Co-Investigator(Renkei-kenkyūsha): OHNISHI Toshio 九州大学, 経済学研究科, 准教授 (60353413)
• Project Period (FY): 2011 – 2013
• Project Status: Completed (Fiscal Year 2013)
• Budget Amount: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000); Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2011: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: Bayes 法 / 事後密度 / 退化型事前分布 / 凸関数 / 予測子 / DIC / ベイズ法 / 弱い事前密度 / 無情報事前密度 / 経験ベイス法 / 分布の裾の重さ / 交叉検証法 / 平滑化 / ２x２分割表

Research Abstract

An unknown hyperparameter is contained in a prior density in the empirical Bayes method. Our primary aim is placed on attempting to evaluate a prior density in terms of a posterior density. We developed the empirical Bayes methods applicable to a wide variety of prior densities. Emphasis is placed on the flexible use of a prior density containing only limited amount of information. Amount of information contained in a prior density is represented through the heaviness of concentration of the density about a fixed point. For this purpose we rigidly define a novel notion of the heaviness of concentration. Further, a likelihood of a Bayesian model based on a mixture of sampling density is introduced. It may be surprising that any formal definition of such a likelihood is not found at all in existing literature. At the final stage of the present research it becomes apparent that our approach is applicable to an important problem of combining evidences from different sources.

Research Products

• [Journal Article] Powerful test of two proportions by (2015)
  • Author(s): Ogura, T. and Yanagimoto, T.
  • Journal Title: Comm. In Statist., Computat. Simul. Volume: To appear
  • Peer Reviewed
• [Journal Article] Permissible boundary prior function as a virtually proper prior density (2015)
  • Author(s): Yanagimoto, T. and Ohnishi, T.
  • Journal Title: Ann. Inst. Statist. Math. Volume: To appear
  • NAID: 40020116671
  • Peer Reviewed
• [Journal Article] Partial order of concentration about a position for comparing Bayesian prior densities (2015)
  • Author(s): Yanagimoto, T. and Ohnishi, T.
  • Journal Title: Far East J. Theoret. Statist. Volume: To appear
  • Peer Reviewed
• [Journal Article] Twofold structure of duality in Bayesian model averaging (2013)
  • Author(s): Ohnishi, T. and Yanagimoto, T
  • Journal Title: J. Japan. Statist. Soc Volume: 43 Pages: 29-55
  • NAID: 10031185799
  • Peer Reviewed
• [Journal Article] Performance of a Bayesian predictorbased procedure of an additional trial after a non- significant result (2013)
  • Author(s): Yanagimoto, T. and Kobayashi, C
  • Journal Title: Lecture Notes in Engin. and Comput. Sci. WCE2013 Volume: vol.I Pages: 291-294
  • Peer Reviewed
• [Journal Article] Partial order of concentration about a position for comparing Bayesian prior densities (2013)
  • Author(s): Yanagimoto, T. and Ohnishi, T
  • Journal Title: Far East J. Theoret. Statist Volume: 45 Pages: 111-132
  • Peer Reviewed
• [Journal Article] Twofold structure of duality in Bayesian model averaging (2013)
  • Author(s): Ohnishi, T. and Yanagimoto, T.
  • Journal Title: Journal of Japanese Statististical Society Volume: 43 Pages: 0-0
  • NAID: 10031185799
  • Peer Reviewed
• [Journal Article] Permissible boundary prior function as a virtually proper prior density. (2012)
  • Author(s): Yanagimoto, T. and Ohnishi, T.
  • Journal Title: ISM-Reaerch Memorandum-1159 Volume: 0 Pages: 0-0
  • NAID: 40020116671
• [Journal Article] Saddlepoint condition on a predictor to reconfirm the need for the assumption of a prior distribution (2011)
  • Author(s): Yanagimoto, T. and Ohnishi, T
  • Journal Title: J. Statist. Plann. Inf Volume: 41 Pages: 1990-2000
  • Peer Reviewed
• [Journal Article] Twofold structure of duality in Bayesian model averaging (2011)
  • Author(s): Ohnishi, T. and Yanagimoto, T.
  • Journal Title: ISM-Reaerch Memorandum Volume: 1148 Pages: 1-10
  • NAID: 10031185799
• [Journal Article] Powerful test of two proportions by assuming a registered prior density
  • Author(s): Ogura, T. and Yanagimoto, T
  • Journal Title: Comm. In Statist., Comput. Simul Volume: (To appear)
  • Peer Reviewed
• [Journal Article] Permissible boundary prior function as a virtually proper prior density Ann
  • Author(s): Yanagimoto, T. and Ohnishi, T
  • Journal Title: Inst. Statist. Math Volume: (To appear)
  • Peer Reviewed
• [Journal Article] 事実の認定を支える証拠と公的な判断
  • Author(s): 柳本武美
  • Journal Title: 「法廷のための統計リ テラシー」, 近代科学社 Volume: (印刷中)
• [Presentation] ある混合の下でのベイスモデルの尤度 (2014)
  • Author(s): 柳本武美 ・ 大西俊郎
  • Organizer: 第13回西東京統計研究会
  • Place of Presentation: 中央大学
• [Presentation] 事前分布の選択とその受容 : ビッグデータ・疎なデータへの対応 (2013)
  • Author(s): 柳本武美
  • Organizer: 科研費研究集会
  • Place of Presentation: 東北大学
  • Year and Date: 2013-12-06
• [Presentation] 信用水準検定のMcNemar検定への適用 (2013)
  • Author(s): 小椋透・ 柳本武美
  • Organizer: 日本計算機統計学会
  • Place of Presentation: 崇城大学ホール・熊本市
  • Year and Date: 2013-11-16
• [Presentation] Bayes予測における尤度最大化とシャノン・エントロピー最大化の双対性 (2013)
  • Author(s): 大西俊郎・柳本武美
  • Organizer: 2013年度統計関連学会連合大会
  • Place of Presentation: 大阪大学
  • Year and Date: 2013-09-08
• [Presentation] 弱い事前情報が繋ぐ情報なし/情報あり事前分布 (2013)
  • Author(s): 柳本武美・大西俊郎
  • Organizer: 2013年度統計関連学会連合大会
  • Place of Presentation: 大阪大学
  • Year and Date: 2013-09-08
• [Presentation] Dual roles of maximizing likelihood and Shannon entropy in Bayesian prediction (2013)
  • Author(s): Ohnishi, T. and Yanagimoto, T
  • Organizer: The 59th WSC
  • Place of Presentation: HKCEC, Hong Kong
  • Year and Date: 2013-08-29
• [Presentation] Examining the Role of a Noninformative Prior Function Through Weakly Informative Prior Densities (2013)
  • Author(s): Yanagimoto, T. and Ohnishi, T
  • Organizer: The 59th WSC
  • Place of Presentation: HKCEC, Hong Kong
  • Year and Date: 2013-08-29
• [Presentation] Performance of a Bayesian Predictor- Based Procedure of an Additional Trial After a Non- Significant Result (2013)
  • Author(s): Yanagimoto, T. and Kobayashi, C
  • Organizer: WCE 2013, ICCSDE
  • Place of Presentation: ICL, London, UK
  • Year and Date: 2013-07-05
• [Presentation] Designing an additional trial after a nonsignificant result : a Bayesian predictor-based procedure (2012)
  • Author(s): Yanagimoto, T
  • Organizer: IBC
  • Place of Presentation: Kobe KICC
  • Year and Date: 2012-08-28
• [Presentation] Flexible and Powerful Exact Test for Hypotheses of Two Proportions in the Era of Clinical Trial Registration (2012)
  • Author(s): Ogura, T. and Yanagimoto, T
  • Organizer: IBC
  • Place of Presentation: Kobe KICC
  • Year and Date: 2012-08-27
• [Presentation] Dual saddlepoint equalities in model averaging and their implication (2012)
  • Author(s): Ohnishi, T. and Yanagimoto, T
  • Organizer: ims-APRM2012
  • Place of Presentation: Tsukuba
  • Year and Date: 2012-07-03
• [Presentation] 臨床試験登録が担保する事前分布の柔軟な仮定 (2012)
  • Author(s): 柳本武美, 小椋透, 小林千鶴
  • Organizer: 日本計量生物学会年会
  • Place of Presentation: 統計数理研究所
  • Year and Date: 2012-05-26
• [Presentation] 検定統計量としての対立仮説モデルのベイズ信用度 (2012)
  • Author(s): 柳本武美
  • Organizer: 統計関連学会連合大会
  • Place of Presentation: 北海道大学
• [Presentation] Permissive boundary prior function as a virtually proper prior density (2012)
  • Author(s): Yanagimoto, T
  • Organizer: ISBA
  • Place of Presentation: Kyoto
• [Presentation] e-混合予測子に基づいた交叉検証法 (2011)
  • Author(s): 柳本武美
  • Organizer: 科研研究集会 「数理統計学の新たな展開」
  • Place of Presentation: 筑波国際会議場エポカル
• [Presentation] 鞍点等式とモデル選択 (2011)
  • Author(s): 大西俊郎 ・柳本武美
  • Organizer: 連合統計大会
  • Place of Presentation: 九州大学
• [Presentation] 平滑化階差行列の次数評価における e-混合交叉検証法 (2011)
  • Author(s): 柳本武美
  • Organizer: 連合統計大会
  • Place of Presentation: 九州大学
• [Presentation] Bayesian モデル e-統合：複数の証拠と意見 (2011)
  • Author(s): 柳本武美 ・大西俊郎
  • Organizer: 科研研究集会「生命科学と統計学 」
  • Place of Presentation: 大阪大学基礎工学国際棟
• [Presentation] Dual saddlepoint equalities in model averaging (2011)
  • Author(s): 大西俊郎・柳本武美
  • Organizer: 科研研究集会「生命科学と統計学 」
  • Place of Presentation: 大阪大学基礎工学国際棟
• [Presentation] 有意でない試験を継続するベイズ的視 (2011)
  • Author(s): 小林千鶴・ 鎌倉稔成・ 柳本武美
  • Organizer: 科研研究集会「生命科学と統計学 」
  • Place of Presentation: 大阪大学基礎工学国際棟
• [Presentation] 加熱製袋工程の改善に必要なデータと解析技法 (2011)
  • Author(s): 小松原義彰ら６名中２番目
  • Organizer: 研究集会「数理モデルの産業・諸科学への活用」
  • Place of Presentation: 富士通汐留シティセンター(東京)
• [Presentation] Performance of a Bayesian Predictor-Based Procedure of an Additional Trial After a Non-Significant Result
  • Author(s): T. Yanagimoto and C. Kobayashi
  • Organizer: World Congress of Engineering 2013
  • Place of Presentation: Imperial Colledge London
• [Presentation] Examining the Role of a Non-informative Prior Function Through Weakly Informative Prior Densities
  • Author(s): T. Yanagimoto and T. Ohnishi
  • Organizer: The 59th WSC
  • Place of Presentation: HKCEC, Hong Kong
• [Presentation] Dual roles of maximizing likelihood and Shannon entropy in Bayesian prediction
  • Author(s): T. Ohnishi and T. Yanagimoto
  • Organizer: The 59th WSC
  • Place of Presentation: HKCEC, Hong Kong
• [Presentation] 信用水準検定のMcNemar検定への適用
  • Author(s): 小椋透・柳本武美
  • Organizer: 日本計算機統計学会 第27回シンポジウﾑ
  • Place of Presentation: 崇城大学
• [Presentation] 事前分布の選択とその受容
  • Author(s): 柳本武美
  • Organizer: 科研集会「大規模での推定・検定・予測法の研究」
  • Place of Presentation: 東北大学
• [Presentation] ある混合の下でのベイスモデルの尤度
  • Author(s): 柳本武美・大西俊郎
  • Organizer: 第13回西東京統計研究会
  • Place of Presentation: 中央大学
• [Presentation] 柔軟な臨床試験のデザインとBayes法
  • Author(s): 小林千鶴 (中央大学) 鎌倉稔成 (中央大学) 柳本武美 (中央大学)
  • Organizer: 応用統計学会2012年度年会
  • Place of Presentation: 統計数理研究所
• [Presentation] 臨床試験登録が担保する事前分布の柔軟な仮定
  • Author(s): 柳本武美 (中央大）小椋透 (中央大） 小林千鶴 (中央大）
  • Organizer: 計量生物学会2012年度年会
  • Place of Presentation: 統計数理研究所
• [Presentation] Permissive boundary prior function as a virtually proper prior density
  • Author(s): Yanagimoto, T. and Ohnishi, T.
  • Organizer: ISBA2012 (国際ベイズ解析学会)
  • Place of Presentation: 京都テルサ
• [Presentation] Dual saddlepoint equalities in model averaging and their implication
  • Author(s): Ohnishi, T., Dunn, P. and Yanagimoto, T.
  • Organizer: imsAPRM2012 会議
  • Place of Presentation: 筑波 エポカル
• [Presentation] Designing an additional trial after a non-significant result: a Bayesian predictor-based procedure
  • Author(s): Yanagimoto, T.
  • Organizer: IBC2012(国際計量生物学会)
  • Place of Presentation: 神戸国際会議場
• [Presentation] Flexible and powerful exact tests of two proportions based on the posterior probability of the alternative model
  • Author(s): Ogura, T., Kamakura T. and Yanagimoto, T.
  • Organizer: IBC2012(国際計量生物学会)
  • Place of Presentation: 神戸国際会議場
• [Presentation] Twofold structure of duality in Bayesian model averaging
  • Author(s): 大西俊郎 (九州大） 柳本武美 (中央大）
  • Organizer: 連合統計大会
  • Place of Presentation: 北海道大学
• [Presentation] 検定統計量としての対立仮説モデルのベイズ信用度 平成24年 9月 11日
  • Author(s): 柳本武美 (中央大)
  • Organizer: 連合統計大会
  • Place of Presentation: 北海道大学
• [Presentation] 再試験を許容する検定法の性能と拡張
  • Author(s): 小林千鶴 (中央大学) 鎌倉稔成 (中央大学) 柳本武美 (中央大学)
  • Organizer: 科研研究集会「医学統計と数理の接点を探る 」
  • Place of Presentation: 南山大学
• [Presentation] 比較試験で informative 事前分布を仮定する試み
  • Author(s): 柳本武美 (中央大)
  • Organizer: 科研研究集会「医学統計と数理の接点を探る 」
  • Place of Presentation: 南山大学
• [Presentation] Twofold structure of duality in Bayesian model averaging： Continuous case
  • Author(s): 大西俊郎 (九州大） 柳本武美 (中央大）
  • Organizer: 科研研究集会「統計的推測とその応用:正則と非正則
  • Place of Presentation: 東海大学
• [Book] 事実の認定を支える証拠と公的な判断. 「法廷のための統計リテラシー」 (2014)
  • Author(s): 柳本武美ら
  • Total Pages: 320
  • Publisher: 近代科学社
• [Remarks] なし