Projected Pólya Tree
Luis Enrique Nieto-Barajas, Gabriel Núñez‐Antonio · Journal of Computational and Graphical Statistics · 2021
One way of defining probability distributions for circular variables (directions in two dimensions) is to radially project probability distributions, originally defined on R2, to the unit circle. Projected distributions have proved to be useful in the study of circular and directional data. Although any bivariate distribution can be used to produce a projected circular model, these distributions are typically parametric. In this article, we consider a bivariate Pólya tree on R2 and project it to the unit circle to define a new Bayesian nonparametric model for circular data. We study the properties of the proposed model, obtain its posterior characterization and show its performance with simulated and real datasets. Supplemental materials for this article are available online.