Related papers: An intermediate distribution between Gaussian and …
The statistics of multi-field inflation are investigated using the stochastic approach. We analytically obtain the probability distribution function of fields with the scaling approximation by extending the previous work by Amendola. The…
A decision must often be made between heavy-tailed and Gaussian errors for a regression or a time series model, and the t-distribution is frequently used when it is assumed that the errors are heavy-tailed distributed. The performance of…
We establish novel rates for the Gaussian approximation of random deep neural networks with Gaussian parameters (weights and biases) and Lipschitz activation functions, in the wide limit. Our bounds apply for the joint output of a network…
We propose a novel, theoretically-grounded, acquisition function for Batch Bayesian optimization informed by insights from distributionally ambiguous optimization. Our acquisition function is a lower bound on the well-known Expected…
We study the rescaled probability distribution of the critical depinning force of an elastic system in a random medium. We put in evidence the underlying connection between the critical properties of the depinning transition and the extreme…
We analyze the Gaussian approximation as a method to obtain the first and second moments of a stochastic process described by a master equation. We justify the use of this approximation with ideas coming from van Kampen's expansion approach…
This paper investigates the problem of Gaussian approximation for the wireless multi-access interference distribution in large spatial wireless networks. First, a principled methodology is presented to establish rates of convergence of the…
In this paper we consider Bayesian estimation for the parameters of inverse Gaussian distribution. Our emphasis is on Markov Chain Monte Carlo methods. We provide complete implementation of the Gibbs sampler algorithm. Assuming an…
The Tsallis $q$-Gaussian distribution is a powerful generalization of the standard Gaussian distribution and is commonly used in various fields, including non-extensive statistical mechanics, financial markets and image processing. It…
In the present study examines the statistical structure of the generated randomized density of the normal distribution and the Cauchy distribution. The study put the allegation that a randomized probability density of the normal…
We derive the joint probability distribution of the first two spectral moments for the G$\beta$E random matrix ensembles in N dimensions for any N. This is achieved by making use of two complementary invariants of the domain in…
In Bayesian inference for mixture models with an unknown number of components, a finite mixture model is usually employed that assumes prior distributions for mixing weights and the number of components. This model is called a mixture of…
We discuss concrete examples for frame functions and their associated density operators, as well as for non-Gleason type probability measures.
The impact of the third (skewness) and fourth (kurtosis) reduced centered moments on the statistical modeling of E1 lines in complex atomic spectra is investigated through the use of Gram-Charlier, Normal Inverse Gaussian and Generalized…
Nonparametric Bayesian models are used routinely as flexible and powerful models of complex data. Many times, a statistician may have additional informative beliefs about data distribution of interest, e.g., its mean or subset components,…
Computer models are widely used in science and engineering to simulate complex systems. However, these models are affected by several sources of uncertainty, which may limit their use for decision making in risk management. We present a…
Multivariate probability density functions of returns are constructed in order to model the empirical behavior of returns in a financial time series. They describe the well-established deviations from the Gaussian random walk, such as an…
Data which lie in the space $\mathcal{P}_{m\,}$, of $m \times m$ symmetric positive definite matrices, (sometimes called tensor data), play a fundamental role in applications including medical imaging, computer vision, and radar signal…
Financial studies require volatility based models which provides useful insights on risks related to investments. Stochastic volatility models are one of the most popular approaches to model volatility in such studies. The asset returns…
The implementation of Bayesian predictive procedures under standard normal models is considered. Two distributions are of particular interest, the K-prime and K-square distributions. They also give exact inferences for simple and multiple…