相关论文: Constructing a multivariate distribution function …
Copulas are a fundamental tool for modelling multivariate dependencies in data, forming the method of choice in diverse fields and applications. However, the adoption of existing models for multimodal and high-dimensional dependencies is…
Copulas are mathematical objects that fully capture the dependence structure among random variables and hence, offer a great flexibility in building multivariate stochastic models. In statistics, a copula is used as a general way of…
Estimating copulas with discrete marginal distributions is challenging, especially in high dimensions, because computing the likelihood contribution of each observation requires evaluating $2^{J}$ terms, with $J$ the number of discrete…
The popular choice of using a $direct$ forecasting scheme implies that the individual predictions do not contain information on cross-horizon dependence. However, this dependence is needed if the forecaster has to construct, based on…
Copulas are used to construct joint distributions in many areas. In some problems, it is necessary to deal with correlation structures that are more complicated than the commonly known copulas. A finite order multivariate Hermite polynomial…
The distributional transform (DT) is amongst the computational methods used for estimation of high-dimensional multivariate normal copula models with discrete responses. Its advantage is that the likelihood can be derived conveniently under…
Quantitative studies in many fields involve the analysis of multivariate data of diverse types, including measurements that we may consider binary, ordinal and continuous. One approach to the analysis of such mixed data is to use a copula…
We address an important yet challenging problem - modeling high-dimensional dependencies across multivariates such as financial indicators in heterogeneous markets. In reality, a market couples and influences others over time, and the…
Univariate and multivariate normal probability distributions are widely used when modeling decisions under uncertainty. Computing the performance of such models requires integrating these distributions over specific domains, which can vary…
In this paper we propose a method for the approximation of high-dimensional functions over finite intervals with respect to complete orthonormal systems of polynomials. An important tool for this is the multivariate classical analysis of…
Computational hardness assumption from the syndrome decoding problem has been useful in designing the security of code based cryptosystem that are safe against quantum computing. Due to complexities in solution using high degree linearized…
We propose a new approach towards approximating the density-to-pair-density map based on copula theory from statistics. We extend the copula theory to multi-dimensional marginals, and deduce that one can describe any (exact or approximate)…
Regular vine copulas can describe a wider array of dependency patterns than the multivariate Gaussian copula or the multivariate Student's t copula. This paper presents two contributions related to model selection of regular vine copulas.…
Bayes spaces were initially designed to provide a geometric framework for the modeling and analysis of distributional data. It has recently come to light that this methodology can be exploited to provide an orthogonal decomposition of…
Data with uncertain, missing, censored, and correlated values are commonplace in many research fields including astronomy. Unfortunately, such data are often treated in an ad hoc way in the astronomical literature potentially resulting in…
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 introduce a novel perspective by linking ordered probabilistic choice to copula theory, a mathematical framework for modeling dependencies in multivariate distributions. Each representation of ordered probabilistic choice behavior can be…
The univariate Piecing-Together approach (PT) fits a univariate generalized Pareto distribution (GPD) to the upper tail of a given distribution function in a continuous manner. A multivariate extension was established by Aulbach et al.…
We propose stepwise variational inference (VI) with vine copulas: a universal VI procedure that combines vine copulas with a novel stepwise estimation procedure of the variational parameters. Vine copulas consist of a nested sequence of…
We propose a new variational Bayes estimator for high-dimensional copulas with discrete, or a combination of discrete and continuous, margins. The method is based on a variational approximation to a tractable augmented posterior, and is…