Fully Nonparametric Regression for Bounded Data Using Dependent Bernstein Polynomials

Abstract

We propose a novel class of probability models for sets of predictor-dependent probability distributions with bounded domain. The proposal extends the Dirichlet–Bernstein prior for single density estimation, by using dependent stick-breaking processes. A general model class and two simplified versions are discussed in detail. Appealing theoretical properties such as continuity, association structure, marginal distribution, large support, and consistency of the posterior distribution are established for all models. The behavior of the models is illustrated using simulated and real-life data. The simulated data are also used to compare the proposed methodology to existing methods. Supplementary materials for this article are available online.