On the small sample behavior of Dirichlet process mixture models for data supported on compact intervals

Abstract

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.

Keywords:

• Density estimation
• Random Bernstein polynomials
• Mixture of beta distributions
• Bayesian nonparametrics
• Posterior convergence rate

Acknowledgements

The first author was supported by the “Programa de Becas de Postgrado de Chile, CONICYT”. The second author was supported by Fondecyt 1180640 grant and by Millennium Science Initiative of the Ministry of Economy, Development, and Tourism, grant “Millennium Nucleus Center for the Discovery of Structures in Complex Data”. The third author was supported by NSF ACI 1443014 grant. The authors thank “Departamento Administrativo de Planeación Municipal del Municipio de Cali” and to “Universidad del Valle”, for providing the solid waste data.

Additional information

Funding

C. Wehrhahn’s research was supported by the “Programa de Becas de Postgrado de Chile, CONICYT”. A. Jara’s research was supported by Fondecyt 1180640 grant and by Millennium Science Initiative of the Ministry of Economy, Development, and Tourism, grant “Millennium Nucleus Center for the Discovery of Structures in Complex Data”. A. F. Barrientos’s research was supported by NSF ACI 1443014 grant. Fondo Nacional de Desarrollo Científico y Tecnológico.