Statistical inference on discrete patterns on random structures
| Project/Area Number |
22540159
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kansai University |
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Principal Investigator |
AKI Sigeo 関西大学, システム理工学部, 教授 (90132696)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | 統計数学 / 条件付き確率母関数 / 離散パターン / DAG / グラフィカルモデル / システムの信頼度 / マルコフ性 / 生存時間 / 連 / クーポン集め問題 / 可換性 / De Finetti の定理 / 順位付け / 尤度比検定 / 対称群 / 隣接リスト / システムの信頼性 / 連続システム / de Finetti測度 / Fibonacci多項式 / マーク付き点過程 / 可換系列 / 経験分布関数 / オーダーkの離散分布 / Markov可換性 / 確率母関数 |
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| Research Abstract |
Main results of the research are as follows. A method for deriving exact distributions of numbers of discrete patterns observed on undirected graphical models is proposed. Parametric statistical models are proposed for observed discrete patterns on exchangeable or partially exchangeable sequences of trials. The mixing measures of the exchangeable sequences also obtained. Further, a parametric statistical model on the permutation group is proposed by using the coupon collecter's problems. The statistical model is useful for statistical inference of ranking data such as maximum likelihood estimation and likelihood ratio tests.
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Report
(5 results)
Research Products
(19 results)
