Department of Mathematics,
Graduate School of Science, Kobe University
Division : Applied Mathematics
Building B, Room 320

Personal Website

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 :
  1. T.Hibi et al, Groebner Bases : Statistics and Software Systems , Springer, 2013.
  2. 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, 117 (2013) 296-312 .
  3. 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), 639--658.