We propose a comprehensive Bayesian approach for graphical model determination in observational studies that can accommodate binary, ordinal or continuous variables simultaneously. Our new models are called copula Gaussian graphical models (CGGMs) and embed graphical model selection inside a semiparametric Gaussian copula. The domain of applicability of our methods is very broad and encompass m...

Copulas were introduced by Sklar [13] to capture the stochastic dependence structure of random variables. Recall that for n ≥ 2, a function C : [0, 1] → [0, 1] is called an n-dimensional copula (n-copula, for short) whenever it is a restriction of an ndimensional distribution function with all univariate margins uniformly distributed on [0, 1]. Hence an n-copula is characterized by the properties:

We propose a comprehensive Bayesian approach for graphical model determination in observational studies that can accommodate binary, ordinal or continuous variables simultaneously. Our new models are called copula Gaussian graphical models (CGGMs) and embed graphical model selection inside a semiparametric Gaussian copula. The domain of applicability of our methods is very broad and encompasses...

We present a reformulation of the information bottleneck (IB) problem in terms of copula, using the equivalence between mutual information and negative copula entropy. Focusing on the Gaussian copula we extend the analytical IB solution available for the multivariate Gaussian case to distributions with a Gaussian dependence structure but arbitrary marginal densities, also called meta-Gaussian d...

Copulas and frailty models are important tools to model bivariate survival data. Equivalence between Archimedean copula models and shared frailty models, e.g., between the Clayton-Oakes copula model and the shared gamma frailty model, has often been claimed in the literature. In this note we show that, in both models, there is indeed the well known equivalence between the copula functions; the ...

Copula modeling has taken the world of finance and insurance, and well beyond, by storm. Why is this? In this paper I review the early start of this development, discuss some important current research, mainly from an applications point of view, and comment on potential future developments. An alternative title of the paper would be “Demystifying the copula craze”. The paper also contains what ...

We propose a comprehensive Bayesian approach for graphical model determination in observational studies that can accommodate binary, ordinal or continuous variables simultaneously. Our new models are called copula Gaussian graphical models (CGGMs) and embed graphical model selection inside a semiparametric Gaussian copula. The domain of applicability of our methods is very broad and encompasses...

We develop sampling algorithms for multivariate Archimedean copulas. For exchangeable copulas, where there is only one generating function, we first analyse the distribution of the copula itself, deriving a number of integral representations and a generating function representation. One of the integral representations is related, by a form of convolution, to the distribution whose Laplace trans...

This paper presents an analysis of Irish clefting couched within LexicalFunctional Grammar. In Irish, cleft sentences are formed using two syntactic permutations. First, a copula is introduced, taking the clefted phrase or word as a predicate. Second, a relative clause is formed containing the remaining material of the original sentence. This basic pattern is valid across a variety of languages...