The Bayesian method is widely used to identify a joint distribution, which is modeled by marginal distributions and a copula. The joint distribution can be identified by one-step procedure, which directly tests all candidate joint distributions, or by two-step procedure, which first identifies marginal distributions and then copula. The weight-based Bayesian method using two-step procedure and the Markov chain Monte Carlo (MCMC)-based Bayesian method using one-step and two-step procedures were recently developed. In this paper, the one-step weight-based Bayesian method and two-step MCMC-based Bayesian method using the parametric marginal distributions are proposed. Comparison studies among the Bayesian methods have not been thoroughly carried out. In this paper, the weight-based and MCMC-based Bayesian methods using one-step and two-step procedures are compared to see which Bayesian method accurately and efficiently identifies a correct joint distribution through simulation studies. It is validated that the two-step weight-based Bayesian method has the best performance.