The aim of this project is to develop Bayesian methods for the analysis of multivariate categorical data. In particular, we are interested in inferring dependence relations between categorical variables, also accounting for possible heterogeneity related to latent clustering structures in the data. We adopt graphical models to represent dependence relations between variables: specifically, a graphical model is a probabilistic model for a collection of random variables based on a graph structure. The complete report can be found here.