Developments of the theory and applications of the expected Euler characteristic method and related mathematics

2021 Fiscal Year Final Research Report

• Project/Area Number: 16H02792
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Statistical science
• Research Institution: The Institute of Statistical Mathematics
• Principal Investigator: Kuriki Satoshi 統計数理研究所, 数理・推論研究系, 教授 (90195545)
• Project Period (FY): 2016-04-01 – 2021-03-31
• Keywords: 確率場 / 多重比較 / 積分幾何学 / 同時信頼領域 / 応用ホモロジー / ランダム行列 / ミンコフスキー汎関数

Outline of Final Research Achievements

The expected Euler characteristic method is a geometric method to approximate the distribution of the maximum of a random field. It is available for the adjustment of the multiplicity p-value in multiple comparisons including signal detection and change point analysis. For example, it is used as a standard tool in brain image data analysis. However, this method has some immature parts as a methodology; e.g., the evaluation of approximation errors has not been fully elucidated. There is also room for further practical improvements such as efficient numerical calculations. Furthermore, it is possible to explore boundaries with related mathematical fields such as the random matrix theory and the theory of algebraic statistics. In this study, we comprehensively study the expected Euler characteristic method from these viewpoints.

Free Research Field

統計科学

Academic Significance and Societal Importance of the Research Achievements

データに基づく発見，すなわち統計的発見においては，常にデータのばらつきに起因する偽陽性の可能性を念頭におく必要がある．ここで偽陽性とは再現性のない発見ということができる．本研究課題である期待オイラー標数法は，偽陽性の確率を見積もるために用いられている典型的な方法であり，その適用範囲の拡大や誤差評価法の確立が望まれていた．