Department of Mathematics,
Graduate School of Science, Kobe University
Division : Applied Mathematics
|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 D-modules.
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), 217--242.
- Tamio Koyama and Akimichi Takemura, Calculation of orthant probabilities by the holonomic gradient method,
Japan Journal of Industrial and Applied Mathematics,32 (2015), 187--204.
- T. Koyama, H. Nakayama, K. Nishiyama, and N. Takayama. Holonomic gradient descent for the fisher-bingham distribution on the d-dimensional sphere,
Computational Statistics, 29 (2014), 661--683.