Stochastic models for partitions and the developments in Bayesian data analysis
| Project/Area Number |
15K05013
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | The Institute of Statistical Mathematics |
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Principal Investigator |
Shuhei Mano 統計数理研究所, 数理・推論研究系, 准教授 (20372948)
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | 統計数学 / 応用数学 / データ解析 / 組み合わせ確率過程 / 計算代数 / 代数統計 / ベイズ統計 |
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| Outline of Final Research Achievements |
Stochastic models of partitions, or random Young diagrams, are bases of Bayesian data analysis and classification. Based on probabilistic and algebraic frameworks, I have investigated models and given methods for computer-aided data analysis. For a jump process which is a dual to a process of partition, a bi-orthogonal expansion of the transition density was provided. For a class of partitions associated with Bell polynomials, the statistical inference was considered with focusing on the A-hypergeometric system defined by Gelfand et al. The maximum likelihood estimation was discussed by using the information geometry of polytopes. Samplers are inevitable for data analysis. By using Groebner bases of a ring of differential operators, a direct sampling algorithm was provided for a broad class of discrete stochastic models including partitions.
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| Academic Significance and Societal Importance of the Research Achievements |
自然数分割の確率モデルの研究では興味の重点が理論的性質にありましたが，本研究は計算機を援用したデータ解析の方法論を考察したことに特徴があります．特に，本研究では分割を含む広いクラスの離散確率モデルについて直接抽出のアルゴリズムを与えました．このことにより従来はマルコフ連鎖モンテカルロ法(MCMC)が唯一の選択肢と考えられてきたモデルからのサンプリングについても原理的には直接抽出が可能になり，MCMCが目的とする分布をマルコフ連鎖の定常分布として実現することに起因する原理的限界を直接抽出により打破できる可能性が示されました．
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Report
(5 results)
Research Products
(41 results)
