Mixture models with decreasing weights

Decreasing weight prior distributions for mixture models play an important role in nonparametric Bayesian inference. Various random probability measures with decreasing weights have been previously explored and it has shown that they provide efficient alternative to the more traditional Dirichlet process model. This ordering of implicitly alleviates so-called label switching problem, as larger correspond groups. A general procedure define any model based on a characterization discrete variable which also allows easy generic sampling algorithm estimating is provided. An exact representation number expected components given. Finally, performance simulated data sets investigated numerically.