7 citations · 22 across the 9 of their papers we have counts for
9 papers
Holonomic Gradient Method for Two Way Contingency Tables
Yoshihito Tachibana, Yoshiaki Goto, Tamio Koyama +1
The holonomic gradient method gives an algorithm to efficiently and accurately evaluate normalizing constants and their derivatives. We apply the holonomic gradient method in the c…
An integral formula for the powered sum of the independent, identically and normally distributed random variables
Tamio Koyama
The distribution of the sum of r-th power of standard normal random variables is a generalization of the chi-squared distribution. In this paper, we represent the probability densi…
Holonomic gradient method for the probability content of a simplex region with a multivariate normal distribution
Tamio Koyama
We use the holonomic gradient method to evaluate the probability content of a simplex region under a multivariate normal distribution. This probability equals to the integral of th…
The Annihilating Ideal of the Fisher Integral
Tamio Koyama
In this paper, we discuss a system of differential equations for the Fisher integral on the special orthogonal group. Especially, we explicitly give a set of linear differential op…
Holonomic modules associated with multivariate normal probabilities of polyhedra
Tamio Koyama
The probability content of a convex polyhedron with a multivariate normal distribution can be regarded as a real analytic function. We give a system of linear partial differential…
Calculation of orthant probabilities by the holonomic gradient method
Tamio Koyama, Akimichi Takemura
We apply the holonomic gradient method (HGM) introduced by [9] to the calculation of orthant probabilities of multivariate normal distribution. The holonomic gradient method applie…
The Holonomic Rank of the Fisher-Bingham System of Differential Equations
Tamio Koyama, Hiromasa Nakayama, Kenta Nishiyama +1
The Fisher-Bingham system is a system of linear partial differential equations satisfied by the Fisher-Bingham integral for the -dimensional sphere . The system is given in…
Holonomic Gradient Descent for the Fisher-Bingham Distribution on the -dimensional Sphere
Tamio Koyama, Hiromasa Nakayama, Kenta Nishiyama +1
We propose an accelerated version of the holonomic gradient descent and apply it to calculating the maximum likelihood estimate (MLE) of the Fisher-Bingham distribution on a -di…
A Holonomic Ideal Annihilating the Fisher-Bingham Integral
Tamio Koyama
We calculate the integration ideal of annihilating differential operators of the non-normalized Fisher-Bingham distribution and show that the ideal agrees with the set of operators…