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Bayesian methods for partial stochastic orderings

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  • Peter D. Hoff

Abstract

We discuss two methods of making nonparametric Bayesian inference on probability measures subject to a partial stochastic ordering. The first method involves a nonparametric prior for a measure on partially ordered latent observations, and the second involves rejection sampling. Computational approaches are discussed for each method, and interpretations of prior and posterior information are discussed. An application is presented in which inference is made on the number of independently segregating quantitative trait loci present in an animal population. Copyright Biometrika Trust 2003, Oxford University Press.

Suggested Citation

  • Peter D. Hoff, 2003. "Bayesian methods for partial stochastic orderings," Biometrika, Biometrika Trust, vol. 90(2), pages 303-317, June.
  • Handle: RePEc:oup:biomet:v:90:y:2003:i:2:p:303-317
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    Cited by:

    1. Beom Seuk Hwang & Zhen Chen, 2015. "An Integrated Bayesian Nonparametric Approach for Stochastic and Variability Orders in ROC Curve Estimation: An Application to Endometriosis Diagnosis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 923-934, September.
    2. Chris Hans & David B. Dunson, 2005. "Bayesian Inferences on Umbrella Orderings," Biometrics, The International Biometric Society, vol. 61(4), pages 1018-1026, December.
    3. Cristina Rueda & Miguel Fernández & Bonifacio Salvador, 2009. "Bayes Discriminant Rules with Ordered Predictors," Journal of Classification, Springer;The Classification Society, vol. 26(2), pages 201-225, August.
    4. Michael L. Pennell & David B. Dunson, 2008. "Nonparametric Bayes Testing of Changes in a Response Distribution with an Ordinal Predictor," Biometrics, The International Biometric Society, vol. 64(2), pages 413-423, June.
    5. 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.

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