Related papers: Non-Gaussian Chi-squared method with the multivari…
The statistical meaning of the local non-Gaussianity parameters f_NL and g_NL is examined in detail. Their relations to the skewness and the kurtosis of the probability distribution of density fluctuations are shown to obey simple fitting…
This paper focuses on inhomogeneous quadratic tests, which involve the sum of a dependent non-central chi-square with a Gaussian random variable. Unfortunately, no closed-form expression is available for the statistical distribution of the…
Bayesian Poisson probability distributions for the average n can be analytically converted into equivalent chi-squared distributions. These can then be combined with other Gaussian or Bayesian Poisson distributions to make a total…
As a step towards a more accurate modelling of redshift-space distortions in galaxy surveys, we develop a general description of the probability distribution function of galaxy pairwise velocities within the framework of the so-called…
The recently proposed non-Gaussian Mat\'{e}rn random field models, generated through Stochastic Partial differential equations (SPDEs), are extended by considering the class of Generalized Hyperbolic processes as noise forcings. The models…
We use the local curvature to investigate the possible existence of non-Gaussianity/asymmetry in the WMAP data. Considering the full sky we find results which are consistent with the Gaussian assumption. However, strong non-Gaussian…
We establish higher-order nonasymptotic expansions for a difference between probability distributions of sums of i.i.d. random vectors in a Euclidean space. The derived bounds are uniform over two classes of sets: the set of all Euclidean…
This study is to investigate the feasibility of least square method in fitting non-Gaussian noise data. We add different levels of the two typical non-Gaussian noises, L\'evy and stretched Gaussian noises, to exact value of the selected…
Many application domains such as ecology or genomics have to deal with multivariate non Gaussian observations. A typical example is the joint observation of the respective abundances of a set of species in a series of sites, aiming to…
Due to gravitational instability, an initially Gaussian density field develops non-Gaussian features as the Universe evolves. The most prominent non-Gaussian features are massive haloes, visible as clusters of galaxies. The distortion of…
In this paper, we develop a non-asymptotic local normal approximation for multinomial probabilities. First, we use it to find non-asymptotic total variation bounds between the measures induced by uniformly jittered multinomials and the…
In this article, we propose the use of partitioning and clustering methods as an alternative to Gaussian quadrature for stochastic collocation. The key idea is to use cluster centers as the nodes for collocation. In this way, we can extend…
I propose a method to fit the probability distribution function (hereafter PDF) of the large scale density field rho, motivated by a Lagrangian version of the continuity equation. It consists in applying the Edgeworth expansion to the…
Distributional regression is extended to Gaussian response vectors of dimension greater than two by parameterizing the covariance matrix $\Sigma$ of the response distribution using the entries of its Cholesky decomposition. The more common…
The paper considers the distribution of a general linear combination of central and non-central chi-square random variables by exploring the branch cut regions that appear in the standard Laplace inversion process. Due to the original…
The distribution of the spin directions of galaxies has been a question in the past decade, with numerous Earth-based and space-based experiments showing that the distribution is not necessarily random. These experiments were based on…
Overdispersed count data are modelled with likelihood and non-likelihood approaches. Likelihood approaches include the Poisson mixtures with three distributions, the gamma, the lognormal, and the inverse Gaussian distributions.…
The primary science driver for 3D galaxy surveys is their potential to constrain cosmological parameters. Forecasts of these surveys' effectiveness typically assume Gaussian statistics for the underlying matter density, despite the fact…
We present exact formulas for both the expected number and the height distribution of local maxima (peaks) in two distinct categories of smooth, non-centered Gaussian fields: (i) nonstationary Gaussian processes and (ii) stationary planar…
Expanding a lower-dimensional problem to a higher-dimensional space and then projecting back is often beneficial. This article rigorously investigates this perspective in the context of finite mixture models, namely how to improve inference…