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Bayesian nonparametric k-sample tests for censored and uncensored data


  • Chen, Yuhui
  • Hanson, Timothy E.


Polya tree priors are random probability distributions that are easily centered at standard parametric families, such as the normal. As such, they provide a convenient avenue toward creating a parametric/nonparametric test statistic “blend” for the classic problem of testing whether data distributions are the same across several subpopulations. Test-statistics that are (empirical) Bayes factors constructed from independent Polya tree priors are proposed. The Polya tree centering distributions are Gaussian with parameters estimated from the data and the p-values are obtained through the permutation of group membership indicators. Generalizations to censored and multivariate data are provided. The conceptually simple test statistic fares surprisingly well against competitors in simulations.

Suggested Citation

  • Chen, Yuhui & Hanson, Timothy E., 2014. "Bayesian nonparametric k-sample tests for censored and uncensored data," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 335-346.
  • Handle: RePEc:eee:csdana:v:71:y:2014:i:c:p:335-346
    DOI: 10.1016/j.csda.2012.11.003

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    References listed on IDEAS

    1. Fay, Michael P. & Shaw, Pamela A., 2010. "Exact and Asymptotic Weighted Logrank Tests for Interval Censored Data: The interval R Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 36(i02).
    2. Hanson T. & Johnson W.O., 2002. "Modeling Regression Error With a Mixture of Polya Trees," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1020-1033, December.
    3. Timothy E. Hanson & Athanasios Kottas & Adam J. Branscum, 2008. "Modelling stochastic order in the analysis of receiver operating characteristic data: Bayesian non-parametric approaches," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 57(2), pages 207-225.
    4. Hanson, Timothy E., 2006. "Inference for Mixtures of Finite Polya Tree Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1548-1565, December.
    5. Zhang, Jin & Wu, Yuehua, 2007. "k-Sample tests based on the likelihood ratio," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4682-4691, May.
    6. Martínez-Camblor, Pablo & de Uña-Álvarez, Jacobo, 2009. "Non-parametric k-sample tests: Density functions vs distribution functions," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3344-3357, July.
    7. Bharath, Karthik & Dey, Dipak K., 2011. "Test to distinguish a Brownian motion from a Brownian bridge using Polya tree process," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 140-145, January.
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