Browsing by Author "Wehrhahn, Claudia"

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    Dependent Bayesian nonparametric modeling of compositional data using random Bernstein polynomials
    (Institute of Mathematical Statistics, 2022) Wehrhahn, Claudia; Barrientos, Andrés F.; Jara Vallejos, Alejandro Antonio
    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.
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    On the small sample behavior of Dirichlet process mixture models for data supported on compact intervals
    (2019) Wehrhahn, Claudia; Jara Vallejos, Alejandro Antonio; Barrientos, Andrés F.
    Bayesian nonparametric models provide a general framework for flexible statistical modeling of modern complex data sets. We compare a rate-optimal and rate-suboptimal Bayesian nonparametric model for density estimation for data supported on a compact interval, by means of the analyses of simulated and real data. The results show that rate-optimal models are not uniformly better, across sample sizes, with respect to the way in which the posterior mass concentrates around a true model and that suboptimal models can outperform the optimal ones, even for relatively large sample sizes.
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    Posterior convergence rate of a class of Dirichlet process mixture model for compositional data
    (2017) Barrientos, Andrés F.; Jara, Alejandro; Wehrhahn, Claudia