Related papers: Nearly Gaussian random variables and application t…
It is often convenient to use Gaussian blur in studying image quality or in data augmentation pipelines for training convoluional neural networks. Because of their convenience, Guassians are sometimes used as first order approximations of…
The integration of physical relationships into stochastic models is of major interest e.g. in data assimilation. Here, a multivariate Gaussian random field formulation is introduced, which represents the differential relations of the…
The term noncentral moderate deviations is used in the literature to mean a class of large deviation principles that, in some sense, fills the gap between the convergence in probability to a constant (governed by a reference large deviation…
We propose flexible Gaussian representations for conditional cumulative distribution functions and give a concave likelihood criterion for their estimation. Optimal representations satisfy the monotonicity property of conditional cumulative…
The projected normal distribution, also known as the angular Gaussian distribution, is obtained by dividing a multivariate normal random variable $\mathbf{x}$ by its norm $\sqrt{\mathbf{x}^T \mathbf{x}}$. The resulting random variable…
We study distributions of random vectors whose components are second order polynomials in Gaussian random variables. Assuming that the law of such a vector is not absolutely continuous with respect to Lebesgue measure, we derive some…
In this article, we obtain a super-exponential rate of convergence in total variation between the traces of the first $m$ powers of an $n\times n$ random unitary matrices and a $2m$-dimensional Gaussian random variable. This generalizes…
In this paper we extend existing Bayesian methods for variable selection in Gaussian process regression, to select both the regression terms and the active covariates in the spatial correlation structure. We then use the estimated posterior…
One of the most widely used properties of the multivariate Gaussian distribution, besides its tail behavior, is the fact that conditional means are linear and that conditional variances are constant. We here show that this property is also…
A generalization of the classic Gaussian random variable to the family of Multi- Gaussian (MG) random variables characterized by shape parameter M > 0, in addition to the mean and the standard deviation, is introduced. The probability…
Computation of moments of transformed random variables is a problem appearing in many engineering applications. The current methods for moment transformation are mostly based on the classical quadrature rules which cannot account for the…
Predictions of the uncertainty associated with extreme events are a vital component of any prediction system for such events. Consequently, the prediction system ought to be probabilistic in nature, with the predictions taking the form of…
Some recent work on confidence intervals for randomized quasi-Monte Carlo (RQMC) sampling found a surprising result: ordinary Student $t$ 95% confidence intervals based on a modest number of replicates were seen to be very effective and…
With increasing concerns of climate change, renewable resources such as photovoltaic (PV) have gained popularity as a means of energy generation. The smooth integration of such resources in power system operations is enabled by accurate…
Let $X$ be a $d$-dimensional random vector and $X_\theta$ its projection onto the span of a set of orthonormal vectors $\{\theta_1,...,\theta_k\}$. Conditions on the distribution of $X$ are given such that if $\theta$ is chosen according to…
In computational and applied statistics, it is of great interest to get fast and accurate calculation for the distributions of the quadratic forms of Gaussian random variables. This paper presents a novel approximation strategy that…
In this paper, we discuss vector-valued Gaussian processes for the approximation of divergence- or rotation-free functions. We establish the theory for such Gaussian processes, then link the theory to multivariate approximation theory, and…
The cumulative shrinkage process is an increasing shrinkage prior that can be employed within models in which additional terms are supposed to play a progressively negligible role. A natural application is to Gaussian factor models, where…
We derive a Gaussian approximation result for the maximum of a sum of random vectors under $(2+\iota)$-th moments. Our main theorem is abstract and nonasymptotic, and can be applied to a variety of statistical learning problems. The proof…
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…