Related papers: Approximation Multivariate Distribution with pair …
In this paper, we address the problem of approximating a multivariate function defined on a general domain in $d$ dimensions from sample points. We consider weighted least-squares approximation in an arbitrary finite-dimensional space $P$…
We show how to construct the implied copula process of response values from a Bayesian additive regression tree (BART) model with prior on the leaf node variances. This copula process, defined on the covariate space, can be paired with any…
We collect well known and less known facts about the bivariate normal distribution and translate them into copula language. In addition, we prove a very general formula for the bivariate normal copula, we compute Gini's gamma, and we…
Vine copulas are a flexible class of dependence models consisting of bivariate building blocks and have proven to be particularly useful in high dimensions. Classical model distance measures require multivariate integration and thus suffer…
The task of approximating a function of d variables from its evaluations at a given number of points is ubiquitous in numerical analysis and engineering applications. When d is large, this task is challenged by the so-called curse of…
This paper proposes famillies of multimatricvariate and multimatrix variate distributions based on elliptically contoured laws in the context of real normed division algebras. The work allows to answer the following inference problems about…
When methods of moments are used for identification of power spectral densities, a model is matched to estimated second order statistics such as, e.g., covariance estimates. If the estimates are good there is an infinite family of power…
We present computational methods for constructing orthogonal/orthonormal polynomials over arbitrary polygonal domains in $\mathbb{R}^2$ using bivariate spline functions. Leveraging a mature MATLAB implementation which generates spline…
Model selection is an important activity in modern data analysis and the conventional Bayesian approach to this problem involves calculation of marginal likelihoods for different models, together with diagnostics which examine specific…
We propose to use nonparametric Bernstein copulas as bivariate pair-copulas in high-dimensional vine models. The resulting smooth and nonparametric vine copulas completely obviate the error-prone need for choosing the pair-copulas from…
To quantify the uncertainty in numerical weather prediction (NWP) forecasts, ensemble prediction systems are utilized. Although NWP forecasts continuously improve, they suffer from systematic bias and dispersion errors. To obtain well…
Empirical copula functions can be used to model the dependence structure of multivariate data. The Greenwald and Khanna algorithm is adapted in order to provide a space-memory efficient approximation to the empirical copula function of a…
Rigby & Stasinopoulos (2005) introduced generalized additive models for location, scale and shape (GAMLSS) where the response distribution is not restricted to belong to the exponential family and its parameters can be specified as…
Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required…
Dense retrieval models use bi-encoder network architectures for learning query and document representations. These representations are often in the form of a vector representation and their similarities are often computed using the dot…
This invited feature article introduces and provides an extensive simulation study of a new Approximate Bayesian Computation (ABC) framework for estimating the posterior distribution and the maximum likelihood estimate (MLE) of the…
In this paper we establish a multivariate exchangeable pairs approach within the framework of Stein's method to assess distributional distances to potentially singular multivariate normal distributions. By extending the statistics into a…
Copulas have now become ubiquitous statistical tools for describing, analysing and modelling dependence between random variables. Sklar's theorem, "the fundamental theorem of copulas", makes a clear distinction between the continuous case…
Copula-based models provide a great deal of flexibility in modelling multivariate distributions, allowing for the specifications of models for the marginal distributions separately from the dependence structure (copula) that links them to…
The problem of overdispersion in multivariate count data is a challenging issue. Nowadays, it covers a central role mainly due to the relevance of modern technologies data, such as Next Generation Sequencing and textual data from the web or…