| Project/Area Number |
19500233
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Statistical science
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| Research Institution | The University of Tokyo |
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Principal Investigator |
HISAYUKI Hara The University of Tokyo, 大学院・工学系研究科, 助教 (40312988)
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| Co-Investigator(Kenkyū-buntansha) |
竹村 彰通 東京大学, 大学院・情報理工学系研究科, 教授 (10171670)
土谷 隆 統計数理研究所, 数理推測研究系, 教授 (00188575)
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| Co-Investigator(Renkei-kenkyūsha) |
TAKEMURA Akimichi 東京大学, 大学院・情報理工学系研究科, 教授 (10171670)
TAKASHI Tsuchiya 政策研究大学院大学, 政策研究科, 教授 (00188575)
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| Project Period (FY) |
2007 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 多変量解析 / 計算代数統計学 / 分割表 / グラフィカルモデル / 縮小推定 / ベイズ推定 / マルコフ基底 / コーダルグラフ / 部分マルコフ基底 / 比例反復法 / 許容性 / 正確検定 / 局所計算 / 個票秘匿 |
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| Research Abstract |
This project focuses mainly on the following problems in the inference of the graphical model, (i) conditional exact tests of goodness-of-fit of the model with Markov bases (ii) localization of the algorithms of the inference (iii) Bayes estimation of parameters. We obtained the following results. (i) In many practical toric models we give explicit forms of Markov bases and proposed algorithms of conditional exact tests by using them. (ii) We proposed a localized algorithm of the iterative propotional scaling for computing the maximum likelihood estimator of a covariance matrix in Gauss graphical models. (iii) We proposed some Bayes admissible estimators of cell probabilities for Poisson decomposable graphical models.
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