Dependent Bayesian nonparametric modeling of compositional data using random Bernstein polynomials
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Date
2022
Journal Title
Journal ISSN
Volume Title
Publisher
Institute of Mathematical Statistics
Abstract
We discuss Bayesian nonparametric procedures for the regression analysis of compositional responses, that is, data supported on a multivariate simplex. The procedures are based on a modified class of multivariate Bernstein polynomials and on the use of dependent stick-breaking processes. A general model and two simplified versions of the general model are discussed. Appealing theoretical properties such as continuity, association structure, support, and consistency of the posterior distribution are established. Additionally, we exploit the use of spike-and-slab priors for choosing the version of the model that best adapts to the complexity of the underlying true data-generating distribution. The performance of the proposed model is illustrated in a simulation study and in an application to solid waste data from Colombia.
Description
Keywords
Density regression, dependent Dirichlet processes, Dirichlet process, Fully nonparametric regression