2018 Fiscal Year Final Research Report
Innovation in statistics and related mathematics through computational algebraic statistics
| Project/Area Number |
25220001
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| Research Category |
Grant-in-Aid for Scientific Research (S)
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| Allocation Type | Single-year Grants |
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| Research Field |
Statistical science
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| Research Institution | Shiga University (2015-2018)
The University of Tokyo (2013-2014) |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
高山 信毅 神戸大学, 理学研究科, 教授 (30188099)
日比 孝之 大阪大学, 情報科学研究科, 教授 (80181113)
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| Project Period (FY) |
2013-05-31 – 2018-03-31
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| Keywords | 統計的推測 / 計算代数統計 |
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| Outline of Final Research Achievements |
In this project we showed that practical computations for many problems, for which existing methods were not feasible, can be performed using the methodology of computational algebraic statistics. In particular we obtained some important results from the theoretical as well as applied viewpoint on the Holonomic Gradient Method, which was proposed by the principal investigator about 8 years ago. Importance of these results were acknowledged by the Analysis Prize of the Mathematical Society of Japan in 2015. By challenging classical difficult problems in mathematical statistics from the viewpoint of algebra, some useful results in algebra have also been obtained. In this sense, the project bridged computation, algebra and statistics. Our results were published in many papers. In addition, the results were implemented in a package for R and provided to the users of statistics.
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| Free Research Field |
情報学
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| Academic Significance and Societal Importance of the Research Achievements |
本研究は課題名にあるように「計算」「代数」「統計」の3つの領域にかかわる研究分野である。より具体的には、1)数値計算、2)グレブナー基底の理論に基づく代数学と代数計算、3)数理統計学の分布論への応用、の3領域であり、本研究での成果はこれらの分野に複合的な効果をもたらした。特にホロノミック勾配法については、その実装において代数計算と数値計算をうまく組み合わせることにより高い性能を出すことがわかり、代数計算の有用性と限界が明らかになった。また応用面では、統計学のみならず無線通信分野における成果が得られたことにも、本研究の有用性があらわれている。
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