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Bayesian nonparametric inference on stochastic ordering

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  • David B. Dunson
  • Shyamal D. Peddada

Abstract

We consider Bayesian inference about collections of unknown distributions subject to a partial stochastic ordering. To address problems in testing of equalities between groups and estimation of group-specific distributions, we propose classes of restricted dependent Dirichlet process priors. These priors have full support in the space of stochastically ordered distributions, and can be used for collections of unknown mixture distributions to obtain a flexible class of mixture models. Theoretical properties are discussed, efficient methods are developed for posterior computation using Markov chain Monte Carlo simulation and the methods are illustrated using data from a study of DNA damage and repair. Copyright 2008, Oxford University Press.

Suggested Citation

  • David B. Dunson & Shyamal D. Peddada, 2008. "Bayesian nonparametric inference on stochastic ordering," Biometrika, Biometrika Trust, vol. 95(4), pages 859-874.
    • Handle: RePEc:oup:biomet:v:95:y:2008:i:4:p:859-874
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    File URL: http://hdl.handle.net/10.1093/biomet/asn043
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    Citations

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    Cited by:

    1. Tomasz Rychlik, 2019. "Sharp bounds on distribution functions and expectations of mixtures of ordered families of distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 166-195, March.
    2. Chuanhua Xing & David B Dunson, 2011. "Bayesian Inference for Genomic Data Integration Reduces Misclassification Rate in Predicting Protein-Protein Interactions," PLOS Computational Biology, Public Library of Science, vol. 7(7), pages 1-10, July.
    3. 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.
    4. Bassetti, Federico & Casarin, Roberto & Leisen, Fabrizio, 2011. "Beta-product Poisson-Dirichlet Processes," DES - Working Papers. Statistics and Econometrics. WS 12160, Universidad Carlos III de Madrid. Departamento de Estadística.
    5. Yeonseung Chung & David Dunson, 2011. "The local Dirichlet process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(1), pages 59-80, February.
    6. Kelter, Riko, 2022. "Power analysis and type I and type II error rates of Bayesian nonparametric two-sample tests for location-shifts based on the Bayes factor under Cauchy priors," Computational Statistics & Data Analysis, Elsevier, vol. 165(C).
    7. Bhattacharya, Abhishek & Dunson, David, 2012. "Nonparametric Bayes classification and hypothesis testing on manifolds," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 1-19.

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