Related papers: On the Voigt profile and its dual
We present a new Bayesian methodology to learn the unknown material density of a given sample by inverting its two-dimensional images that are taken with a Scanning Electron Microscope. An image results from a sequence of projections of the…
A Vogan superdiagram is a set of involution and painting on a Dynkin diagram. It selects a real form, or equivalently an involution, from a complex simple Lie superalgebra. We introduce the double Vogan superdiagram, which is two sets of…
We explore the finite dimensional distributions of the second-order scattering transform of a class of non-Gaussian processes when all the scaling parameters go to infinity simultaneously. For frequently used wavelets, we find a coupling…
An image or volume of interest in positron emission tomography (PET) is reconstructed from pairs of gamma rays emitted from a radioactive substance. Many image reconstruction methods are based on estimation of pixels or voxels on some…
The Wigner-Ville distribution (WVD) and quaternion offset linear canonical transform (QOLCT) are a useful tools in signal analysis and image processing. The purpose of this paper is to define the Wigner-Ville distribution associated with…
Gaussian graphical models have received considerable attention during the past four decades from the statistical and machine learning communities. In Bayesian treatments of this model, the G-Wishart distribution serves as the conjugate…
This paper studies fundamental aspects of modelling data using multivariate Watson distributions. Although these distributions are natural for modelling axially symmetric data (i.e., unit vectors where $\pm \x$ are equivalent), for…
This paper studies identifiability and convergence behaviors for parameters of multiple types in finite mixtures, and the effects of model fitting with extra mixing components. First, we present a general theory for strong identifiability,…
We investigate the low-dimensional structure of deterministic transformations between random variables, i.e., transport maps between probability measures. In the context of statistics and machine learning, these transformations can be used…
The statistical distribution of eigenvalues of pairs of coupled random matrices can be expressed in terms of integral kernels having a generalized Christoffel--Darboux form constructed from sequences of biorthogonal polynomials. For…
The univariate generalized extreme value (GEV) distribution is the most commonly used tool for analyzing the properties of rare events. The ever greater utilization of Bayesian methods for extreme value analysis warrants detailed…
We provide a new general theorem for multivariate normal approximation on convex sets. The theorem is formulated in terms of a multivariate extension of Stein couplings. We apply the results to a homogeneity test in dense random graphs and…
Regression models for dichotomous data are ubiquitous in statistics. Besides being useful for inference on binary responses, these methods serve also as building blocks in more complex formulations, such as density regression, nonparametric…
A computer simulation model is used to study the density profile and flow of a miscible gaseous fluid mixture consisting of differing constituent masses ($m_A = m_B/3$) through an open matrix. The density profile is found to decay with the…
Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settings, is to determine the mixture order and estimate the…
We consider Gaussian ensembles of m N x N complex matrices. We identify an enhanced symmetry in the system and the resultant closed subsector, which is naturally associated with the radial sector of the theory. The density of radial…
We study statistical properties of a class of band random matrices which naturally appears in systems of interacting particles. The local spectral density is shown to follow the Breit-Wigner distribution in both localized and delocalized…
Metabolic heterogeneity is widely recognised as the next challenge in our understanding of non-genetic variation. A growing body of evidence suggests that metabolic heterogeneity may result from the inherent stochasticity of intracellular…
The stacked density profile of cosmic voids in the galaxy distribution provides an important tool for the use of voids for precision cosmology. We study the density profiles of voids identified using the ZOBOV watershed transform algorithm…
We show that density models describing multiple observables with (i) hard boundaries and (ii) dependence on external parameters may be created using an auto-regressive Gaussian mixture model. The model is designed to capture how observable…