Developing statistical models representing diversity

2020 Fiscal Year Final Research Report

• Project/Area Number: 18K13454
• Research Category: Grant-in-Aid for Early-Career Scientists
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 12040:Applied mathematics and statistics-related
• Research Institution: Kyushu University (2020); The University of Tokyo (2018-2019)
• Principal Investigator: Tsukuda Koji 九州大学, 数理学研究院, 准教授 (30764972)
• Project Period (FY): 2018-04-01 – 2021-03-31
• Keywords: 統計モデル / 確率分割 / 確率過程 / 共分散行列 / 適合度検定 / 統計的漸近理論 / 無限次元空間における弱収束 / ランダム組み合わせ構造

Outline of Final Research Achievements

This project aims to study random partition models used for representing statistical diversities from the viewpoint of mathematical properties and develop a new random partition model. In particular, we investigated approximations and asymptotic evaluations associated with the Ewens sampling formula and the Pitman sampling formula. Moreover, we proposed a discrimination analysis method based on the Dirichlet-multinomial model.

Statistical inference for some related stochastic process models and multivariate models were also studied. We discussed and proposed goodness-of-fit tests and change-point tests for stochastic process models. We proposed high-dimensional tests for some typical models of covariance matrices.

Free Research Field

数理統計

Academic Significance and Societal Importance of the Research Achievements

ユーエンス抽出公式やピットマン抽出公式に従う確率分割の挙動をこれまでより正確に評価できるようになり，これらのモデルを応用する場合により詳細な議論が可能になると期待される．また，提案した判別分析法は多様性が高い集団を考える場合に特に有用である．関連するモデルについての研究で得られた成果は，それぞれが独自のアプローチで検定法を考えたものであり，他のモデルへの広がりも期待できる．