We know from above that our conditional posterior View the MathML source is a normal-inverted-gamma-2 density while π(pj|y,z) is Dirichlet. We know all the integrating constants of these densities (see Appendix A of Bauwens et al., 1999). As a by-product of the Gibbs output we have draws of the z so that we can approximate the log of these posterior densities using