# Beta-Binomial stick-breaking non-parametric prior

## TL;DR

This paper introduces the Beta-Binomial stick-breaking process, a new nonparametric prior that generalizes existing models and improves MCMC convergence for density estimation tasks.

## Contribution

It proposes a novel dependent Beta-Binomial stick-breaking prior that encompasses Dirichlet and Geometric processes, enhancing flexibility and computational efficiency.

## Key findings

- The model includes Dirichlet and Geometric processes as special cases.
- A density estimation algorithm is developed and tested successfully.
- The dependence parameter controls label-switching and convergence properties.

## Abstract

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.