Vine copulas are a highly flexible class of dependence models, which are based on the decomposition of the density into bivariate building blocks. For applications one usually makes the simplifying assumption that copulas of conditional distributions are independent of the variables on which they are conditioned. However this assumption has been criticised for being too restrictive. We examine both simplified and non-simplified vine copulas in three dimensions and investigate conceptual differences. We show and compare contour surfaces of three-dimensional vine copula models, which prove to be much more informative than the contour lines of the bivariate marginals. Our investigation shows that non-simplified vine copulas can exhibit arbitrarily irregular shapes, whereas simplified vine copulas appear to be smooth extrapolations of their bivariate margins to three dimensions. In addition to a variety of constructed examples, we also investigate a three-dimensional subset of the well-known uranium data set and visually detect that a non-simplified vine copula is necessary to capture its complex dependence structure.
In many studies multivariate event time data are generated from clusters having a possibly complex association pattern. Flexible models are needed to capture this dependence. Vine copulas serve this purpose. Inference methods for vine copulas are available for complete data. Event time data, however, are often subject to right-censoring. As a consequence, the existing inferential tools, e.g. likelihood estimation, need to be adapted. A two-stage estimation approach is proposed. First, the marginal distributions are modeled. Second, the dependence structure modeled by a vine copula is estimated…
Understanding the dependence relationship of credit spreads of corporate bonds is important for risk management. Vine copula models with tail dependence are used to analyze a credit spread dataset of Chinese corporate bonds, understand the dependence among different sectors and perform conditional inferences. It is shown how the effect of tail dependence affects risk transfer, or the conditional distributions given one variable is extreme. Vine copula models also provide more accurate cross prediction results compared with linear regressions. These conditional inference techniques are a statis…
A bivariate copula mixed model has been recently proposed to synthesize diagnostic test accuracy studies and it has been shown that is superior to the standard generalized linear mixed model (GLMM) in this context. Here we call trivariate vine copulas to extend the bivariate meta-analysis of diagnostic test accuracy studies by accounting for disease prevalence. Our vine copula mixed model includes the trivariate GLMM as a special case and can also operate on the original scale of sensitivity, specificity, and disease prevalence. Our general methodology is illustrated by re-analysing the data o…
Systems subject to uncertain inputs produce uncertain responses. Uncertainty quantification (UQ) deals with the estimation of statistics of the system response, given a computational model of the system and a probabilistic model of its inputs. In engineering applications it is common to assume that the inputs are mutually independent or coupled by a Gaussian or elliptical dependence structure (copula). In this paper we overcome such limitations by modelling the dependence structure of multivariate inputs as vine copulas. Vine copulas are models of multivariate dependence built from simpler pai…
A recent paper proposed an extended trivariate generalized linear mixed model (TGLMM) for synthesis of diagnostic test accuracy studies in the presence of non-evaluable index test results. Inspired by the aforementioned model we propose an extended trivariate vine copula mixed model that includes the TGLMM as special case, but can also operate on the original scale of sensitivity, specificity, and disease prevalence. The performance of the proposed vine copula mixed model is examined by extensive simulation studies in comparison with the TGLMM. Simulation studies showed that the TGLMM overesti…
There is an extensive literature on methods for meta-analysis of diagnostic studies, but it mainly focuses on a single test. However, the better understanding of a particular disease has led to the development of multiple tests. A multinomial generalized linear mixed model (GLMM) is recently proposed for the joint meta-analysis of studies comparing multiple tests. We propose a novel model for the joint meta-analysis of multiple tests, which assumes independent multinomial distributions for the counts of each combination of test results in diseased and non-diseased patients, conditional on the …
Measuring interdependence between probabilities of default (PDs) in different industry sectors of an economy plays a crucial role in financial stress testing. Thereby, regression approaches may be employed to model the impact of stressed industry sectors as covariates on other response sectors. We identify vine copula based quantile regression as an eligible tool for conducting such stress tests as this method has good robustness properties, takes into account potential nonlinearities of conditional quantile functions and ensures that no quantile crossing effects occur. We illustrate its perfo…
Stationary and ergodic time series can be constructed using an s-vine decomposition based on sets of bivariate copula functions. The extension of such processes to infinite copula sequences is considered and shown to yield a rich class of models that generalizes Gaussian ARMA and ARFIMA processes to allow both non-Gaussian marginal behaviour and a non-Gaussian description of the serial partial dependence structure. Extensions of classical causal and invertible representations of linear processes to general s-vine processes are proposed and investigated. A practical and parsimonious method for …
The heterogeneous autoregressive (HAR) model is revised by modeling the joint distribution of the four partial-volatility terms therein involved. Namely, today's, yesterday's, last week's and last month's volatility components. The joint distribution relies on a (C-) Vine copula construction, allowing to conveniently extract volatility forecasts based on the conditional expectation of today's volatility given its past terms. The proposed empirical application involves more than seven years of high-frequency transaction prices for ten stocks and evaluates the in-sample, out-of-sample and one-st…
For a particular disease there may be two diagnostic tests developed, where each of the tests is subject to several studies. A quadrivariate generalized linear mixed model (GLMM) has been recently proposed to joint meta-analyse and compare two diagnostic tests. We propose a D-vine copula mixed model for joint meta-analysis and comparison of two diagnostic tests. Our general model includes the quadrivariate GLMM as a special case and can also operate on the original scale of sensitivities and specificities. The method allows the direct calculation of sensitivity and specificity for each test, a…
While there is considerable effort to identify signaling pathways using linear Gaussian Bayesian networks from data, there is less emphasis of understanding and quantifying conditional densities and probabilities of nodes given its parents from the identifed Bayesian network. Most graphical models for continuous data assume a multivariate Gaussian distribution, which might be too restrictive. We re-analyse data from an experimental setting considered in Sachs et al. (2005) to illustrate the effects of such restrictions. For this we propose a novel non Gaussian nonlinear structural equation mod…
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 forecasts of future atmospheric states. To assess uncertainty in NWP forecasts so-called forecast ensembles are utilized. They are generated by employing a NWP model for distinct variants. However, as forecast ensembles are not able to capture the full amount of uncertainty in an NWP model, they often exhibit biases and dispersion errors. Therefore it has become com…
With the advancements of computer architectures, the use of computational models proliferates to solve complex problems in many scientific applications such as nuclear physics and climate research. However, the potential of such models is often hindered because they tend to be computationally expensive and consequently ill-fitting for uncertainty quantification. Furthermore, they are usually not calibrated with real-time observations. We develop a computationally efficient algorithm based on variational Bayes inference (VBI) for calibration of computer models with Gaussian processes. Unfortuna…
Floods are the most common and among the most severe natural disasters in many countries around the world. As global warming continues to exacerbate sea level rise and extreme weather, governmental authorities and environmental agencies are facing the pressing need of timely and accurate evaluations and predictions of flood risks. Current flood forecasts are generally based on historical measurements of environmental variables at monitoring stations. In recent years, in addition to traditional data sources, large amounts of information related to floods have been made available via social medi…
Computed tomography (CT) can capture volumes large enough to measure a statistically meaningful number of micron-sized particles with a sufficiently good resolution to allow for the analysis of individual particles. However, the development of methods to efficiently investigate such image data and interpretably model the observed particle features is still an active field of research. When image data of particles exhibiting a wide range of shapes and sizes is considered, traditional image segmentation methods, such as the classic watershed algorithm, struggle to recognize particles with satisf…
This paper intends to develop tools for characterizing non-linear spectral dependence between spontaneous brain signals. We use parametric copula models (both bivariate and vine models) applied on the magnitude of Fourier coefficients rather than using coherence. The motivation behind this work is an experiment on rats that studied the impact of stroke on the connectivity structure (dependence) between local field potentials recorded at various channels. We address the following major questions. First, we ask whether one can detect any changepoint in the regime of a brain channel for a given f…
CopulaSMOTE: A Copula-Based Oversampling Approach for Imbalanced Classification in Diabetes Prediction
Stanford University School of Medicine（斯坦福大学医学院）；Minnesota State University（明尼苏达州立大学）；University of Louisiana at Lafayette（路易斯安那大学拉斐特分校）；Southern Utah University（犹他州南方大学）
