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Bayesian nonparametric inference of stochastically ordered distributions, with Pólya trees and Bernstein polynomials

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  • Karabatsos, George
  • Walker, Stephen G.

Abstract

We introduce approaches to performing Bayesian nonparametric statistical inference for distribution functions exhibiting a stochastic ordering. We consider Pólya tree prior distributions, and Bernstein polynomial prior distributions, and each prior provides an appealing and simple way of introducing the stochastic order.

Suggested Citation

  • Karabatsos, George & Walker, Stephen G., 2007. "Bayesian nonparametric inference of stochastically ordered distributions, with Pólya trees and Bernstein polynomials," Statistics & Probability Letters, Elsevier, vol. 77(9), pages 907-913, May.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:9:p:907-913
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    References listed on IDEAS

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    1. Lo Shaw-Hwa, 1987. "Estimation Of Distribution Functions Under Order Restrictions," Statistics & Risk Modeling, De Gruyter, vol. 5(3-4), pages 251-262, April.
    2. El Barmi, Hammou & Dykstra, Richard L., 1994. "Restricted multinomial maximum likelihood estimation based upon Fenchel duality," Statistics & Probability Letters, Elsevier, vol. 21(2), pages 121-130, September.
    3. Peter D. Hoff, 2003. "Bayesian methods for partial stochastic orderings," Biometrika, Biometrika Trust, vol. 90(2), pages 303-317, June.
    4. Ronald E. Gangnon & William N. King, 2002. "Minimum distance estimation of the distribution functions of stochastically ordered random variables," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 51(4), pages 485-492, October.
    5. Alan Gelfand & Athanasios Kottas, 2001. "Nonparametric Bayesian Modeling for Stochastic Order," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(4), pages 865-876, December.
    6. 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, September.
    7. Dykstra, R. L. & Lee, Chu-In Charles & Yan, Xiaosong, 1996. "Multinomial estimation procedures for two stochastically ordered distributions," Statistics & Probability Letters, Elsevier, vol. 30(4), pages 353-361, November.
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    Cited by:

    1. Gard, Charlotte C. & Brown, Elizabeth R., 2015. "A Bayesian hierarchical model for estimating and partitioning Bernstein polynomial density functions," Computational Statistics & Data Analysis, Elsevier, vol. 87(C), pages 73-83.

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