Related papers: On Numerical Estimation of Joint Probability Distr…
A new type of quadrature is developed. The Gaussian quadrature, for a given measure, finds optimal values of a function's argument (nodes) and the corresponding weights. In contrast, the Lebesgue quadrature developed in this paper, finds…
We compute the joint distributions of arbitrary numbers of eigenvectors of real and complex symmetric random tensors by the quantum field theoretical methods which were previously used to compute the mean distributions. We obtain the random…
In this work, we study non-parametric estimation of joint probabilities of a given set of discrete and continuous random variables from their (empirically estimated) 2D marginals, under the assumption that the joint probability could be…
The ability to estimate joint, conditional and marginal probability distributions over some set of variables is of great utility for many common machine learning tasks. However, estimating these distributions can be challenging,…
Normal variance mixtures are a class of multivariate distributions that generalize the multivariate normal by randomizing (or mixing) the covariance matrix via multiplication by a non-negative random variable W. The multivariate t…
Random matrices formed from i.i.d. standard real Gaussian entries have the feature that the expected number of real eigenvalues is non-zero. This property persists for products of such matrices, independently chosen, and moreover it is…
We consider the product of n complex non-Hermitian, independent random matrices, each of size NxN with independent identically distributed Gaussian entries (Ginibre matrices). The joint probability distribution of the complex eigenvalues of…
An expression for the joint probability distribution of the principal curvatures at an arbitrary point in the ensemble of isosurfaces defined on isotropic Gaussian random fields on Rn is derived. The result is obtained by deriving symmetry…
We consider $N\times N$ Hermitian or symmetric random matrices with independent entries. The distribution of the $(i,j)$-th matrix element is given by a probability measure $\nu_{ij}$ whose first two moments coincide with those of the…
A finite dimensional quantum system for which the quantum chaos conjecture applies has eigenstates, which show the same statistical properties than the column vectors of random orthogonal or unitary matrices. Here, we consider the different…
Computation of the marginal likelihood from a simulated posterior distribution is central to Bayesian model selection but is computationally difficult. I argue that the marginal likelihood can be reliably computed from a posterior sample by…
Nowadays, more and more datasets are stored in a distributed way for the sake of memory storage or data privacy. The generalized eigenvalue problem (GEP) plays a vital role in a large family of high-dimensional statistical models. However,…
The generalized inverse Gaussian, denoted $\mathrm{GIG}(p, a, b)$, is a flexible family of distributions that includes the gamma, inverse gamma, and inverse Gaussian distributions as special cases. In addition to its applications in…
For a variant of the algorithm in [Pit19] (arXiv:1903.10816) to compute the approximate density or distribution function of a linear mixture of independent random variables known by a finite sample, it is presented a proof of the functional…
We study the joint probability density of the eigenvalues of a product of rectangular real, complex or quaternion random matrices in a unified way. The random matrices are distributed according to arbitrary probability densities, whose only…
A generalisation of the Ginibre ensemble of non-Hermitian random square matrices is introduced. The corresponding probability measure is induced by the ensemble of rectangular Gaussian matrices via a quadratisation procedure. We derive the…
We consider Bayesian inference problems with computationally intensive likelihood functions. We propose a Gaussian process (GP) based method to approximate the joint distribution of the unknown parameters and the data. In particular, we…
It is shown that the density of the ratio of two random variables with the same variance and joint Gaussian density satisfies a non stationary diffusion equation. Implications of this result for kernel density estimation of the condensed…
The eigenvalues of an arbitrary quaternionic matrix have a joint probability distribution function first derived by Ginibre. We show that there exists a mapping of this system onto a fermionic field theory and then use this mapping to…
We discuss the product of $M$ rectangular random matrices with independent Gaussian entries, which have several applications including wireless telecommunication and econophysics. For complex matrices an explicit expression for the joint…