Open Access
2022 Dependent Bayesian nonparametric modeling of compositional data using random Bernstein polynomials
Claudia Wehrhahn, Andrés F. Barrientos, Alejandro Jara
Author Affiliations +
Electron. J. Statist. 16(1): 2346-2405 (2022). DOI: 10.1214/22-EJS2002


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.

Funding Statement

C. Wehrhahn’s research was supported by the “Programa de Becas de Postgrado de Chile, CONICYT”, NSF-DMS 1738053 and ATD-DMS 1441433. A. Jara’s work was supported by the Agencia Nacional de Investigación y Desarrollo (ANID) through the Fondo Nacional de Desarrollo Científico y Tecnológico (FONDECYT) grant No 1220907 and through grant NCN17_059 from Millennium Science Initiative Program, Millennium Nucleus Center for the Discovery of Structures in Complex Data (MIDAS).


Download Citation

Claudia Wehrhahn. Andrés F. Barrientos. Alejandro Jara. "Dependent Bayesian nonparametric modeling of compositional data using random Bernstein polynomials." Electron. J. Statist. 16 (1) 2346 - 2405, 2022.


Received: 1 August 2021; Published: 2022
First available in Project Euclid: 1 April 2022

MathSciNet: MR4402566
zbMATH: 07524975
Digital Object Identifier: 10.1214/22-EJS2002

Keywords: density regression , dependent Dirichlet processes , Dirichlet process , Fully nonparametric regression

Vol.16 • No. 1 • 2022
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