Department of Mathematics,
Graduate School of Science, Kobe University
Division : Applied Mathematics
|Building B, Room 320|
|Research Field :
Hypergeometric Functions, Computer Algebra (algorithms, applications, and implementations)
|Research Summary :
In the last 5 years, I have studied applications of hypergeometric functions
of several variables to statistics.
The main topic has been the holonomic gradient method
( HGM ),
which is a method to evaluate numerically normalizing constants and
their derivatives of "holonomic" probability distributions.
The theory and algorithms for hypergeometric functions are used for evaluations.
|Primary Publications :|
T.Hibi et al, Groebner Bases : Statistics and Software Systems , Springer, 2013.
- Hiroki Hashiguchi, Yasuhide Numata, Nobuki Takayama, Akimichi Takemura,
Holonomic gradient method for the distribution function of the largest root of a Wishart matrix
Journal of Multivariate Analysis,
Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara,
Tomonari Sei, Nobuki Takayama, Akimichi Takemura,
Holonomic Gradient Descent and its Application to Fisher-Bingham Integral
Advances in Applied Mathematics 47 (2011),