Performance improvements of algebraic statistical methods

2022 Fiscal Year Final Research Report

• Project/Area Number: 18H04092
• Research Category: Grant-in-Aid for Scientific Research (A)
• Allocation Type: Single-year Grants
• Section: 一般
• Review Section: Medium-sized Section 60:Information science, computer engineering, and related fields
• Research Institution: Shiga University
• Principal Investigator: Takemura Akimichi 滋賀大学, 役員, 学長 (10171670)
• Project Period (FY): 2018-04-01 – 2023-03-31
• Keywords: 数理統計学 / 統計的推測 / 漸近理論

Outline of Final Research Achievements

In this project, we have conducted research on performance improvements and practical implementation of methods of algebraic statistics. In particular, we focused on the method, called the holonomic gradient method, which uses partial differential equations with rational function coefficients to compute various integrals and probabilities appearing in statistics. Using the holonomic gradient method, we obtained practical results on the complex Wishart distribution, which appears in wireless communication. We also studied the tube method and obtained result on the tail probability of Wishart distribution under general covariance matrices.

Free Research Field

統計科学

Academic Significance and Societal Importance of the Research Achievements

ホロノミック勾配法は研究代表者が2010年頃に代数学者との共同研究の中から考案した新しい手法であり、統計学で必要とされる計算を高速かつ高精度でおこなうことのできる手法である。この方法は、統計学と代数学の双方で新たな研究テーマとなり、活発な研究が行われ、それ以前は困難と思われていたいくつかの数値計算が可能となった。このような数値計算は、統計学にとどまらず様々な分野の計算に用いることができものである。