相关论文: Holonomic gradient method for the distribution fun…

We study the distribution of the ratio of two central Wishart matrices with different covariance matrices. We first derive the density function of a particular matrix form of the ratio and show that its cumulative distribution function can…

A holonomic system for the probability density function of the largest eigenvalue of a non-central complex Wishart distribution with identity covariance matrix is derived. Furthermore a new determinantal formula for the probability density…

We apply the holonomic gradient method to compute the distribution function of a weighted sum of independent noncentral chi-square random variables. It is the distribution function of the squared length of a multivariate normal random…

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 case of the conditional Poisson or multinomial distribution…

We give a bijection between a quotient space of the parameters and the space of moments for any $A$-hypergeometric distribution. An algorithmic method to compute the inverse image of the map is proposed utilizing the holonomic gradient…

Recently, the school of Takemura and Takayama have developed a quite interesting minimization method called holonomic gradient descent method (HGD). It works by a mixed use of Pfaffian differential equation satisfied by an objective…

In this paper we implement the holonomic gradient method to exactly compute the normalising constant of Bingham distributions. This idea is originally applied for general Fisher-Bingham distributions in Nakayama et al. (2011). In this paper…

A holonomic system of linear partial differential equations is, roughly speaking, a system whose solution space is finite dimensional. A distribution that is a solution of a holonomic system is called a holonomic distribution. We give…

We apply the holonomic gradient method (HGM) introduced by [9] to the calculation of orthant probabilities of multivariate normal distribution. The holonomic gradient method applied to orthant probabilities is found to be a variant of…

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 the probability density function of the multivariate Gaussian…

We study properties of Fisher distribution (von Mises-Fisher distribution, matrix Langevin distribution) on the rotation group SO(3). In particular we apply the holonomic gradient descent, introduced by Nakayama et al. (2011), and a method…

We give a new algorithm to find local maximum and minimum of a holonomic function and apply it for the Fisher-Bingham integral on the sphere $S^n$, which is used in the directional statistics. The method utilizes the theory and algorithms…

In this study, we derive the exact distributions of eigenvalues of a singular Wishart matrix under an elliptical model. We define generalized heterogeneous hypergeometric functions with two matrix arguments and provide convergence…

This paper proposes a unified approach that enables the Wishart distribution to be studied simultaneously in the real, complex, quaternion and octonion cases. In particular, the noncentral generalised Wishart distribution, the joint density…

Natural gradient methods have been used to optimise the parameters of probability distributions in a variety of settings, often resulting in fast-converging procedures. Unfortunately, for many distributions of interest, computing the…

By holonomic guessing, we denote the process of finding a linear differential equation with polynomial coefficients satisfied by the generating function of a sequence, for which only a few first terms are known. Holonomic guessing has been…

This paper discusses certain properties of heterogeneous hypergeometric functions with two matrix arguments. These functions are newly defined but have already appeared in statistical literature and are useful when dealing with the…

We present an algorithm for computing a holonomic system for a definite integral of a holonomic function over a domain defined by polynomial inequalities. If the integrand satisfies a holonomic difference-differential system including…

In the convergence analysis of numerical methods for solving partial differential equations (such as finite element methods) one arrives at certain generalized eigenvalue problems, whose maximal eigenvalues need to be estimated as…

We present fully polynomial approximation schemes for a broad class of Holant problems with complex edge weights, which we call Holant polynomials. We transform these problems into partition functions of abstract combinatorial structures…