A0872
Title: Partially geometric stick-breaking processes
Authors: Gilbert Fellingham - Brigham Young University (United States)
Matthew Heiner - Brigham Young University (United States) [presenting]
Alejandro Jara - Pontificia Universidad Catolica de Chile (Chile)
Garritt Page - Brigham Young University (United States)
Abstract: Empirical distributions for count data often exhibit idiosyncrasies among low values, such as zero inflation and stable tail behavior. A flexible model is proposed for counts that combines nonparametric estimation of early probabilities with fixed decay after a single, unknown change point. A stick-breaking construction is used with variables that are beta distributed before the change point and share a single value thereafter, inducing a geometric tail. The resulting process model parsimoniously balances needed flexibility where data are abundant, with a parametric representation where data are naturally sparse. The construction admits a collapsed posterior distribution for the change point, avoiding transdimensional MCMC. It is illustrated by modeling rally lengths in men's professional tennis, where the change point may indirectly measure the effect of server advantage. Finally, the new process is used to construct a countably infinite mixture model, extending the geometric stick-breaking process of Fuentes-Garcia, Mena, and Walker, and demonstrating its effectiveness for density estimation. The random change point accommodates a variety of behaviors, ranging from a parsimonious approximation of Poisson-Dirichlet process mixtures to mixtures of finite mixtures.
