Bayesian nonparametric k-sample tests for censored and uncensored data
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.
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