2012 Fiscal Year Final Research Report
Theory and practice for inference of high dimensional statistical model with computational algebraic geometry.
| Project/Area Number |
22500252
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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 | Niigata University |
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Principal Investigator |
HARA Hisayuki 新潟大学, 人文社会・教育科学系, 准教授 (40312988)
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| Co-Investigator(Renkei-kenkyūsha) |
TAKEMURA Akimichi 東京大学, 情報理工学系研究科, 教授 (10171670)
KURIKI Satoshi 統計数理研究所, 数理推論研究系, 教授 (90195545)
SEI Tomonari 慶應義塾大学, 理工学研究科, 講師 (20401242)
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| Project Period (FY) |
2010 – 2012
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| Keywords | 分割表 / グラフィカルモデル |
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| Research Abstract |
In this study we derived Markov bases of some practical models for contingency tables such as homogeneous Markov chain model and split model and proposed practical algorithms of exact tests by using these Markov bases. In general, however, it is not easy to obtain an exact list of a Markov basis for a discrete exponential family model. We gave some practical algorithms of exact test also for such models by using some practical subsets of Markov bases or lattice bases and checked that the performances of proposed algorithms are comparable to the ones by using Markov bases.
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