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We discuss Bayesian nonparametric procedures for the regression analysis ofcompositional responses, that is, data supported on a multivariate simplex. Theprocedures are based on a modified class of multivariate Bernstein polynomialsand on the use of dependent stick-breaking processes. A general model and twosimplified versions of the general model are discussed. Appealing theoreticalproperties such as continuity, association structure, support, and consistencyof the posterior distribution are established. Additionally, we exploit the useof spike-and-slab priors for choosing the version of the model that best adaptsto the complexity of the underlying true data-generating distribution. Theperformance of the proposed model is illustrated in a simulation study and inan application to solid waste data from Colombia.

Dependent Bayesian nonparametric modeling of compositional data using random Bernstein polynomials