Stick-Breaking Processes With Exchangeable Length Variables

Abstract

Our object of study is the general class of stick-breaking processes with exchangeable length variables. These generalize well-known Bayesian nonparametric priors in an unexplored direction. We give conditions to assure the respective species sampling process is proper and the corresponding prior has full support. For a rich subclass we explain how, by tuning a single $[0,1]$-valued parameter, the stochastic ordering of the weights can be modulated, and Dirichlet and Geometric priors can be recovered. A general formula for the distribution of the latent allocation variables is derived and an MCMC algorithm is proposed for density estimation purposes.

KEYWORDS:

• Dirichlet process
• Exchangeable sequence
• Geometric process
• Species sampling process
• Stick-breaking

Supplementary Material

Supplement of Stick-breaking processes with exchangeable length variables: The supplemental material delves into technical aspects behind ESBs, including the proof of our main results. An MCMC algorithm is proposed and details of clusters and density estimators are provided. (.pdf file)

Additional information

Funding

The first author was supported by a CONACyT PhD scholarship. Both authors gratefully acknowledge the support of PAPIIT Grant IG100221.