Bayesian inference for discrete regression chain graph models is discussed, specifically for graphs that are Markov equivalent to bi-directed graphs, that is they define the same set of independencies for the joint probability distribution as illustrated in Chap.  2 . Conjugate analysis is applicable only to specific graphical configurations, requiring Markov Chain Monte Carlo techniques for broader applications. The discussion will encompass model specification and estimation, focusing on probability and marginal log-linear parameterizations of the model. The previous issues will be illustrated through real data applications. We additionally discuss the complexities involved in prior specification that is an essential aspect of the Bayesian framework.