2019 Fiscal Year Final Research Report
Study of multi-variable hypergeometric differential equations for statistics
| Project/Area Number |
17K05279
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | Kobe University |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2017-04-01 – 2020-03-31
|
| Keywords | 多変数超幾何関数 / ホロノミック勾配法 / 二元分割表 / Wishart行列 |
|---|
| Outline of Final Research Achievements |
We gave a new algorithm to translate an A-hypergeometric system to a Pfaffian equation. A Pfaffian equation for the matrix 2F1 is derived. We show that the expectation of a random manifold defined by Wishart matrix and its maximal eigenvalue is expressed by an integral. We studied holonomic systems for the integral under several conditions on the Wishart matrix and performed a numerical analysis of them. An error free method to solve systems of difference equations is given. It utilizes the Chinese remainder theorem. It is demonstrated that the method is useful to evaluate the normalizing constant and its derivatives for two way contingency tables.
|
| Free Research Field |
解析学
|
| Academic Significance and Societal Importance of the Research Achievements |
Holonomic 系の Pfaffian 方程式を導出するという古典的な問題に関して, 新しい計算アルゴリズムを与えるとともに, 行列超幾何関数や対称性が高いEuler標数の期待値関数については理論的な結果を得た. これらは統計分布の正規化定数の数値評価問題に適用可能である.
|
