Related papers: A Matrix Gaussian Distribution
The envelope of an elliptical Gaussian complex vector, or equivalently, the amplitude or norm of a bivariate normal random vector has application in many weather and signal processing contexts. We explicitly characterize its distribution in…
Composition of low-dimensional distributions, whose foundations were laid in the papaer published in the Proceeding of UAI'97 (Jirousek 1997), appeared to be an alternative apparatus to describe multidimensional probabilistic models. In…
A general piecewise (including pointwise) probability distribution with space-saving notation and its hierarchical particular cases are considered. The explicit closed-form normalization, expectation, and variance formulas along with the…
The analytic inference, e.g. predictive distribution being in closed form, may be an appealing benefit for machine learning practitioners when they treat wide neural networks as Gaussian process in Bayesian setting. The realistic widths,…
The beta distribution is a basic distribution serving several purposes. It is used to model data, and also, as a more flexible version of the uniform distribution, it serves as a prior distribution for a binomial probability. The bivariate…
We introduce categories of extended Gaussian maps and Gaussian relations which unify Gaussian probability distributions with relational nondeterminism in the form of linear relations. Both have crucial and well-understood applications in…
We compute analytically, for large N, the probability distribution of the number of positive eigenvalues (the index N_{+}) of a random NxN matrix belonging to Gaussian orthogonal (\beta=1), unitary (\beta=2) or symplectic (\beta=4)…
Distribution data refers to a data set where each sample is represented as a probability distribution, a subject area receiving burgeoning interest in the field of statistics. Although several studies have developed…
Matrix-form Poisson probability distributions were recently introduced as one matrix generalization of Panjer distributions. We show in this paper that under the constraint that their representation is to be nonnegative, they have a…
Matrix multivariate Pearson type II-Riesz distribution is defined and some of its properties are studied. In particular, the associated matrix multivariate beta distribution type I is derived. Also the singular values and eigenvalues…
The singular values of products of standard complex Gaussian random matrices, or sub-blocks of Haar distributed unitary matrices, have the property that their probability distribution has an explicit, structured form referred to as a…
Correlation matrices are the sub-class of positive definite real matrices with all entries on the diagonal equal to unity. Earlier work has exhibited a parametrisation of the corresponding Cholesky factorisation in terms of partial…
The Gaussian theory of errors has been generalized to situations, where the Gaussian distribution and, hence, the Gaussian rules of error propagation are inadequate. The generalizations are based on Bayes' theorem and a suitable measure.…
This paper derives the elliptical matrix variate version of the well known univariate Birnbaum and Saunders distribution. A generalisation based on a matrix transformation is proposed, instead of the independent element by element…
Variational Bayesian Inference is a popular methodology for approximating posterior distributions over Bayesian neural network weights. Recent work developing this class of methods has explored ever richer parameterizations of the…
In this paper, we study majorization for probability distributions and column stochastic matrices. We show that majorizations in general can be reduced to the aforementioned sets. We characterize linear operators that preserve majorization…
Matrix-variate distributions can intuitively model the dependence structure of matrix-valued observations that arise in applications with multivariate time series, spatio-temporal or repeated measures. This paper develops an…
A generalized matrix function is a generalization of determinant and permanent function. In this paper, we introduced the formula for the value of a generalized matrix function of a linear sum of permutation matrices. We show that a linear…
The G-Wishart distribution is an essential component for the Bayesian analysis of Gaussian graphical models as the conjugate prior for the precision matrix. Evaluating the marginal likelihood of such models usually requires computing…
The probability of the small deviations of the matrix $AA^T$ determinant is estimated, where $A$ is an $n\times\infty$ random matrix with centered entries having joint Gaussian distribution. The inequality obtained is sharp in a sence.