Tamio KOYAMA 
Tamio KOYAMA
Department of Mathematics,
Graduate School of Science, Kobe University 
Division : Applied Mathematics
Assistant Professor 
Building B, Room 328

Research Field :
Holonomic Gradient Method


Research Summary :
I study applications of the Holonomic gradient method (HGM) to numerical calculation of
normalizing constants and region probability in Statistics.
The HGM is a method of numerical calculation, which is based on the theory and algorithms of Dmodules.
The HGM can be applied to a board class of functions.
In order to apply the HGM to a target function,
we need an explicit form of a system of differential equations for the function,
the "initial value" of the function,
asymptotic properties of the solutions of the system of the differential equations,
and so on.
I also develop softwares utilizing the HGM.


Primary Publications : 

Tamio Koyama, Holonomic modules associated with multivariate normal probabilities of polyhedra,
Funkcialaj Ekvacioj, 59 (2016), 217242.
 Tamio Koyama and Akimichi Takemura, Calculation of orthant probabilities by the holonomic gradient method,
Japan Journal of Industrial and Applied Mathematics,32 (2015), 187204.
 T. Koyama, H. Nakayama, K. Nishiyama, and N. Takayama. Holonomic gradient descent for the fisherbingham distribution on the ddimensional sphere,
Computational Statistics, 29 (2014), 661683.


