Related papers: A Toolbox for the Radial and Angular Marginalizati…
Univariate and multivariate normal probability distributions are widely used when modeling decisions under uncertainty. Computing the performance of such models requires integrating these distributions over specific domains, which can vary…
This paper introduces an extension to the normal distribution through the polar method to capture bimodality and asymmetry, which are often observed characteristics of empirical data. The later two features are entirely controlled by a…
In this paper we develop a very general class of bivariate discrete distributions. The basic idea is very simple. The marginals are obtained by taking the random geometric sum of a baseline distribution function. The proposed class of…
We propose a probability distribution for multivariate binary random variables. The probability distribution is expressed as principal minors of the parameter matrix, which is a matrix analogous to the inverse covariance matrix in the…
This is an up-to-date introduction to, and overview of, marginal likelihood computation for model selection and hypothesis testing. Computing normalizing constants of probability models (or ratio of constants) is a fundamental issue in many…
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,…
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…
The polarization of the cosmic microwave background radiation will have a distribution of singularities and anti-singularities, points where the polarization vanishes for topological reasons. The statistics of polarization singularities…
The regular variation model for multivariate extremes decomposes the joint distribution of the extremes in polar coordinates in terms of the angles and the norm of the random vector as the product of two independent densities: the angular…
This paper develops some objective priors for certain parameters of the bivariate normal distribution. The parameters considered are the regression coefficient, the generalized variance, and the ratio of the conditional variance of one…
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…
We present a probabilistic model that simultaneously learns alignments and distributed representations for bilingual data. By marginalizing over word alignments the model captures a larger semantic context than prior work relying on hard…
The statistical distribution of the ratio of two normal random variables is characterized by its heavy-tailed nature and absence of finite moments. The shape of its density function is highly variable, capable of exhibiting unimodal or…
This article proposes a bivariate Simplex distribution for modeling continuous outcomes constrained to the interval $(0,1)$, which can represent proportions, rates, or indices. We derive analytical expressions to calculate the dependence…
In certain privacy-sensitive scenarios within fields such as clinical trial simulations, federated learning, and distributed learning, researchers often face the challenge of estimating correlations between variables without access to…
In this article, we discuss a bivariate distribution whose conditionals are univariate binomial distributions and the marginals are not binomial that exhibits negative correlation. Some useful structural properties of this distribution…
Fern\'andez-Dur\'an and Gregorio-Dom\'inguez (2014) defined a family of probability distributions for a vector of circular random variables by considering multiple nonnegative trigonometric sums. These distributions are highly flexible and…
Normalisation in probability theory turns a subdistribution into a proper distribution. It is a partial operation, since it is undefined for the zero subdistribution. This partiality makes it hard to reason equationally about normalisation.…
The properties of the normal distribution under linear transformation, as well the easy way to compute the covariance matrix of marginals and conditionals, offer a unique opportunity to get an insight about several aspects of uncertainties…
We provide in this paper simulation algorithms for one-sided and two-sided truncated normal distributions. These algorithms are then used to simulate multivariate normal variables with restricted parameter space for any covariance…