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 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 :
  1. Tamio Koyama, Holonomic modules associated with multivariate normal probabilities of polyhedra, Funkcialaj Ekvacioj, 59 (2016), 217--242.
  2. 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.
  3. 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.