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In this paper, we concentrate on new methodologies for copulas introduced and developed by Joe, Cooke, Bedford, Kurowica, Daneshkhah and others on the new class of graphical models called vines as a way of constructing higher dimensional…

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…

As an important tool in financial risk management, stress testing aims to evaluate the stability of financial portfolios under some potential large shocks from extreme yet plausible scenarios of risk factors. The effectiveness of a stress…

Today weather forecasting is conducted using numerical weather prediction (NWP) models, consisting of a set of differential equations describing the dynamics of the atmosphere. The output of such NWP models are single deterministic…

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…

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…

A novel copula-based multivariate panel ordinal model is developed to estimate structural relations among components of well-being. Each ordinal time-series is modelled using a copula-based Markov model to relate the marginal distributions…

A time-varying bivariate copula joint model, which models the repeatedly measured longitudinal outcome at each time point and the survival data jointly by both the random effects and time-varying bivariate copulas, is proposed in this…

This paper addresses the problem of quantification and propagation of uncertainties associated with dependence modeling when data for characterizing probability models are limited. Practically, the system inputs are often assumed to be…

Copulas are essential tools in statistics and probability theory, enabling the study of the dependence structure between random variables independently of their marginal distributions. Among the various types of copulas, Ratio-Type Copulas…

Signals coming from multivariate higher order conditional moments as well as the information contained in exogenous covariates, can be effectively exploited by rational investors to allocate their wealth among different risky investment…

We introduce new estimates and tests of independence in copula models with unknown margins using $\phi$-divergences and the duality technique. The asymptotic laws of the estimates and the test statistics are established both when the…

Starting from the characterization of extreme-value copulas based on max-stability, large-sample tests of extreme-value dependence for multivariate copulas are studied. The two key ingredients of the proposed tests are the empirical copula…

Modeling of longitudinal data often requires diffusion models that incorporate overall time-dependent, nonlinear dynamics of multiple components and provide sufficient flexibility for subject-specific modeling. This complexity challenges…

Temporal, spatial or spatio-temporal probabilistic models are frequently used for weather forecasting. The D-vine (drawable vine) copula quantile regression (DVQR) is a powerful tool for this application field, as it can automatically…

In this article, a copula-based method for mixed regression models is proposed, where the conditional distribution of the response variable, given covariates, is modelled by a parametric family of continuous or discrete distributions, and…

Following our previous work on copula-based nonsymmetric bivariate dependence measures, we propose a new set of conditions on nonsymmetric multivariate dependence measures which characterize both independence and complete dependence of one…

In many applications it is desirable to infer coarse-grained models from observational data. The observed process often corresponds only to a few selected degrees of freedom of a high-dimensional dynamical system with multiple time scales.…

Real-world deployment of machine learning models is challenging because data evolves over time. While no model can work when data evolves in an arbitrary fashion, if there is some pattern to these changes, we might be able to design methods…

Predicting the dependencies between observations from multiple time series is critical for applications such as anomaly detection, financial risk management, causal analysis, or demand forecasting. However, the computational and numerical…