Beta-Binomial stick-breaking non-parametric prior

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.

Stick-breaking processes with exchangeable length variables

“…If µ defines a DSBp with parameters (β, θ, µ 0 ), we call Φ as in (15) a Dirichlet driven stick-breaking mixture (DSBm) with parameters (β, θ, µ 0 , G). Whenever G(• | s n ) converges weakly to G(• | s), as s n → s in S, the mapping…”

“…for some V = (v i ) i≥1 , taking values in [0, 1], hereinafter referred to as length variables. Although there are models featuring dependent length variables [12,10,9,15], most efforts have concentrated in the case where these are mutually independent [30,27,18]. Our proposal here is to study the class of stick-breaking processes with exchangeable length variables.…”