Hence, the same simplification would apply in a larger joint probability expression such as the one in this model, composed of Dirichlet-multinomial densities plus factors for many other random variables dependent on the values of the categorical variables.
This implies that the same simplification would be relevant to a more intricate joint probability expression like the one depicted in this framework, which incorporates Dirichlet-multinomial distributions along with additional factors accounting for numerous other stochastic variables influenced by the categorical values.