 Suppose that we wanted to draw formula_84 observations from the naive model with exactly formula_52 clusters.A simple algorithm for doing this would be to draw formula_52 values of formula_87 from formula_66, a distribution formula_89 from formula_62 and then for each observation independently sample the cluster formula_51 with probability formula_92 and the value of the observation according to formula_93.It is easy to see that this algorithm does not work in case where we allow infinite clusters because this would require sampling an infinite dimensional parameter formula_94.