Is infinity that far? A Bayesian nonparametric perspective of finite mixture models

Mixture models are one of the most widely used statistical tools when dealing with data from heterogeneous populations. Following a Bayesian nonparametric perspective, we introduce new class priors: Normalized Independent Point Process. We investigate probabilistic properties this and present many special cases. In particular, provide an explicit formula for distribution implied partition, as well posterior characterization process in terms superposition two discrete measures. also consistency results. Moreover, design both marginal conditional algorithm finite mixture random number components. These schemes based on auxiliary variable MCMC, which allows handling otherwise intractable overcomes challenges associated Reversible Jump algorithm. illustrate performance potential our model simulation study real applications.