7 citations · 22 across the 9 of their papers we have counts for
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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…
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…
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…
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…