Dependent Bayesian nonparametric modeling of compositional data using random Bernstein polynomials

TL;DR

This paper introduces a Bayesian nonparametric regression model for compositional data using dependent Bernstein polynomials and stick-breaking processes, with theoretical guarantees and practical applications.

Contribution

It proposes a novel Bayesian nonparametric framework for compositional data analysis based on dependent Bernstein polynomials and introduces model selection via spike-and-slab priors.

Findings

Model exhibits desirable theoretical properties such as continuity and consistency.

Simulation studies demonstrate the model's flexibility and accuracy.

Application to real waste data shows practical effectiveness.

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.