An important problem in modeling real phenomena where several variables are involved is being able to have appropriate probabilistic multivariate models. On the other hand, it is also necessary to have methodologies that allow inferences to be made in these proposed models. From a probabilistic frame, a general approach to propose multivariate models is the use of copulas. However, being able to carry out a joint analysis for all parameters involved in copula models can become a challenging task. In this chapter, we propose an inference approach based on a decomposition of the final distribution. We show how to use that factorization to make joint Bayesian inferences for all parameters in models defined by a copula. The aforementioned approach offers the flexibility to carry out the inference process in two stages: a first stage in which inferences are made for parameters of marginal distributions involved in the corresponding copula, and a second step where inferences are obtained for parameters of the corresponding copula. The procedure is illustrated using simulated data.