Related papers: Modeling high-dimensional dependence among astrono…
The estimation of cosmological parameters from a given data set requires a construction of a likelihood function which, in general, has a complicated functional form. We adopt a Gaussian copula and constructed a copula likelihood function…
Latent Gaussian copula models provide a powerful means to perform multi-view data integration since these models can seamlessly express dependencies between mixed variable types (binary, continuous, zero-inflated) via latent Gaussian…
We present a simple method for assessing the predictive performance of high-dimensional models directly in data space when only samples are available. Our approach is to compare the quantiles of observables predicted by a model to those of…
Context: Statistical properties of the cosmic density fields are to a large extent encoded in the shape of the one-point density probability distribution functions (PDF). In order to successfully exploit such observables, a detailed…
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)…
We introduce the coverage correlation coefficient, a novel nonparametric measure of statistical association designed to quantifies the extent to which two random variables have a joint distribution concentrated on a singular subset with…
Copulas are popular as models for multivariate dependence because they allow the marginal densities and the joint dependence to be modeled separately. However, they usually require that the transformation from uniform marginals to the…
Copulas are powerful statistical tools for capturing dependencies across data dimensions. Applying Copulas involves estimating independent marginals, a straightforward task, followed by the much more challenging task of determining a single…
We propose and demonstrate a joint model of anatomical shapes, image features and clinical indicators for statistical shape modeling and medical image analysis. The key idea is to employ a copula model to separate the joint dependency…
Thanks to their ability to capture complex dependence structures, copulas are frequently used to glue random variables into a joint model with arbitrary marginal distributions. More recently, they have been applied to solve statistical…
Galaxies are often modelled as composites of separable components with distinct spectral signatures, implying that different wavelength ranges are only weakly correlated. They are not. We present a data-driven model which exploits subtle…
This paper investigates the probabilistic properties that determine the existence of space-time transformations between diffusion processes. We prove that two diffusions are related by a monotone space-time transformation if and only if…
A ubiquitous feature of data of our era is their extra-large sizes and dimensions. Analyzing such high-dimensional data poses significant challenges, since the feature dimension is often much larger than the sample size. This thesis…
Variational Bayes methods approximate the posterior density by a family of tractable distributions whose parameters are estimated by optimisation. Variational approximation is useful when exact inference is intractable or very costly. Our…
We generalize 2-Wasserstein dependence coefficients to measure dependence between a finite number of random vectors. This generalization includes theoretical properties, and in particular focuses on an interpretation of maximal dependence…
In actuarial research, a task of particular interest and importance is to predict the loss cost for individual risks so that informative decisions are made in various insurance operations such as underwriting, ratemaking, and capital…
The composite likelihood (CL) is amongst the computational methods used for the estimation of high-dimensional multivariate normal (MVN) copula models with discrete responses. Its computational advantage, as a surrogate likelihood method,…
We discuss the connection between information and copula theories by showing that a copula can be employed to decompose the information content of a multivariate distribution into marginal and dependence components, with the latter…
Copula models have been widely used to model the dependence between continuous random variables, but modeling count data via copulas has recently become popular in the statistics literature. Spearman's rho is an appropriate and effective…
We propose the extension of Fr\'{e}chet-Hoeffding copula bounds for circular data. The copula is a powerful tool for describing the dependency of random variables. In two dimensions, the Fr\'{e}chet-Hoeffding upper (lower) bound indicates…