Bayesian multivariate Bernstein polynomial density estimation
This paper introduces a new approach to Bayesian nonparametric inference for densities on the hypercube, based on the use of a multivariate Bernstein polynomial prior. Posterior convergence rates under the proposed prior are obtained. Furthermore, a novel sampling scheme, based on the use of slice sampling techniques, is proposed for estimation of the posterior predictive density. The approach is illustrated with both simulated and real data examples
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- Lorenzo Trippa & Paolo Bulla & Sonia Petrone, 2011. "Extended Bernstein prior via reinforced urn processes," Annals of the Institute of Statistical Mathematics, Springer, vol. 63(3), pages 481-496, June.
- Axel Tenbusch, 1994. "Two-dimensional Bernstein polynomial density estimators," Metrika, Springer, vol. 41(1), pages 233-253, December.
- Sancetta, Alessio & Satchell, Stephen, 2004. "The Bernstein Copula And Its Applications To Modeling And Approximations Of Multivariate Distributions," Econometric Theory, Cambridge University Press, vol. 20(03), pages 535-562, June.
- Alejandro Jara & Timothy Hanson & Fernando A. Quintana & Peter Müller & Gary L. Rosner, . "DPpackage: Bayesian Semi- and Nonparametric Modeling in R," Journal of Statistical Software, American Statistical Association, vol. 40(i05).
- Sonia Petrone & Larry Wasserman, 2002. "Consistency of Bernstein polynomial posteriors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(1), pages 79-100.
- Omiros Papaspiliopoulos & Gareth O. Roberts, 2008. "Retrospective Markov chain Monte Carlo methods for Dirichlet process hierarchical models," Biometrika, Biometrika Trust, vol. 95(1), pages 169-186.
- Sonia Petrone, 1999. "Random Bernstein Polynomials," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(3), pages 373-393.
- Olkin, Ingram & Liu, Ruixue, 2003. "A bivariate beta distribution," Statistics & Probability Letters, Elsevier, vol. 62(4), pages 407-412, May.
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