Related papers: Selected Methods for non-Gaussian Data Analysis
We discuss the requirements of good statistics for quantifying non-Gaussianity in the Cosmic Microwave Background. The importance of rotational invariance and statistical independence is stressed, but we show that these are sometimes…
This article proposes a graphical model that handles mixed-type, multi-group data. The motivation for such a model originates from real-world observational data, which often contain groups of samples obtained under heterogeneous conditions…
In this work, we propose a non-iterative Gaussian transformation strategy based on copula function, which doesn't require some commonly seen restrictive assumptions in the previous studies such as the elliptically symmetric distribution…
To model high dimensional data, Gaussian methods are widely used since they remain tractable and yield parsimonious models by imposing strong assumptions on the data. Vine copulas are more flexible by combining arbitrary marginal…
Gaussian factor models have proven widely useful for parsimoniously characterizing dependence in multivariate data. There is a rich literature on their extension to mixed categorical and continuous variables, using latent Gaussian variables…
q-Gaussian distribution appear in many science areas where we can find systems that could be described within a nonextensive framework. Usually, a way to assert that these systems belongs to nonextensive framework is by means of numerical…
Learning the joint dependence of discrete variables is a fundamental problem in machine learning, with many applications including prediction, clustering and dimensionality reduction. More recently, the framework of copula modeling has…
The statistical dependencies which independent component analysis (ICA) cannot remove often provide rich information beyond the linear independent components. It would thus be very useful to estimate the dependency structure from data.…
Zero-inflated continuous data ubiquitously appear in many fields, in which lots of exactly zero-valued data are observed while others distribute continuously. Due to the mixed structure of discreteness and continuity in its distribution,…
Non-random sample selection is a commonplace amongst many empirical studies and it appears when an output variable of interest is available only for a restricted non-random sub-sample of data. We introduce an extension of the generalized…
We introduce a data assimilation strategy aimed at accurately capturing key non-Gaussian structures in probability distributions using a small ensemble size. A major challenge in statistical forecasting of nonlinearly coupled multiscale…
Fully describing the entire data set is essential in multivariate risk assessment, since moderate levels of one variable can influence another, potentially leading it to be extreme. Additionally, modelling both non-extreme and extreme…
We propose a novel distributional regression model for a multivariate response vector based on a copula process over the covariate space. It uses the implicit copula of a Gaussian multivariate regression, which we call a ``regression…
We consider graphical models based on a recursive system of linear structural equations. This implies that there is an ordering, $\sigma$, of the variables such that each observed variable $Y_v$ is a linear function of a variable specific…
Verification and validation of fully automated vehicles is linked to an almost intractable challenge of reflecting the real world with all its interactions in a virtual environment. Influential stochastic parameters need to be extracted…
Multivariate time series (MTS) data often include a heterogeneous mix of non-Gaussian distributional features (asymmetry, multimodality, heavy tails) and data types (continuous and discrete variables). Traditional MTS methods based on…
Copulas are functions that describe dependence structures of random vectors, without describing their univariate marginals. In statistics, the separation is sometimes useful, the quality and/or quantity of available information on these two…
Gaussian graphical models (GGMs) are well-established tools for probabilistic exploration of dependence structures using precision matrices. We develop a Bayesian method to incorporate covariate information in this GGMs setup in a nonlinear…
Copulas, generalized estimating equations, and generalized linear mixed models promote the analysis of grouped data where non-normal responses are correlated. Unfortunately, parameter estimation remains challenging in these three…
Research on Poisson regression analysis for dependent data has been developed rapidly in the last decade. One of difficult problems in a multivariate case is how to construct a cross-correlation structure and at the meantime make sure that…