Generalized Mixtures of Finite Mixtures and Telescoping Sampling

Within a Bayesian framework, comprehensive investigation of mixtures finite (MFMs), i.e., with prior on the number components, is performed. This model class has applications in model-based clustering as well for semi-parametric density estimation and requires suitable specifications inference methods to exploit its full potential. We contribute by considering generalized MFMs where hyperparameter ?K symmetric Dirichlet weight distribution depends components. show that this may be regarded non-parametric mixture outside Gibbs-type priors. emphasize distinction between components K clusters K+, filled given data. In MFM model, K+ random variable ?K. employ flexible derive corresponding MFMs. For posterior we propose novel telescoping sampler which allows arbitrary component distributions without resorting reversible jump Markov chain Monte Carlo (MCMC) methods. The explicitly samples but otherwise only usual MCMC steps model. ease application using different demonstrated several data sets.