A new class of nonparametric prior distributions, termed Beta-Binomial stick-breaking process, is proposed. By allowing the underlying length random variables to be dependent through a Beta marginals Markov chain, an appealing discrete random probability measure arises. The chain's dependence parameter controls the ordering of the stick-breaking weights, and thus tunes the model's label-switching ability. Also, by tuning this parameter, the resulting class contains the Dirichlet process and the Geometric process priors as particular cases, which is of interest for fast convergence of MCMC implementations.Some properties of the model are discussed and a density estimation algorithm is proposed and tested with simulated datasets.

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We investigate the general class of stick-breaking processes with exchangeable length variables. These generalize well-known Bayesian non-parametric priors in an unexplored direction. We give conditions to assure the respective species sampling process is discrete almost surely and the corresponding prior has full support. For a rich sub-class we find the probability that the stick-breaking weights are decreasingly ordered. A general formulae for the distribution of the latent allocation variables is derived and an MCMC algorithm is proposed for density estimation purposes.

Gibbs sampling methods for mixture models are based on data augmentation schemes that account for the unobserved partition in the data. Conditional samplers rely on allocation variables that identify each observation with a mixture component. They are known to suffer from slow mixing in infinite mixtures, where some form of truncation, either deterministic or random, is required. In mixtures with random number of components, the exploration of parameter spaces of different dimensions can also be challenging. We tackle these issues by expressing the mixture components in the random order of appearance in an exchangeable sequence directed by the mixing distribution. We derive a sampler that is straightforward to implement for mixing distributions with tractable size-biased ordered weights. In infinite mixtures, no form of truncation is necessary. As for finite mixtures with random dimension, a simple updating of the number of components is obtained by a blocking argument, thus, easing challenges found in trans-dimensional moves via Metropolis-Hasting steps. Additionally, the latent clustering structure of the model is encrypted by means of an ordered partition with blocks labelled in the least element order, which mitigates the label-switching problem. We illustrate through a simulation study the good mixing performance of the new sampler.

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