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Graphical models and copulas are two sets of tools for multivariate analysis. Both are in some sense pathways to the construction of multivariate distributions using modular representations. The former focuses on languages to express conditional independence constraints, factorizations and efficient inference algorithms. The latter allows for the encoding of some marginal features of the joint distribution (univariate marginals, in particular) directly, without resorting to an inference algorithm. In this talk we exploit copula parameterizations in two graphical modeling tasks: parameterizing decomposable models and building proposal distributions for inference with Markov chain Monte Carlo; parameterizing directed mixed graph models and providing simple estimation algorithms based on composite likelihood methods.
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