Abstract: The paper revisits two-sample hypothesis testing problems under Lehmann alternatives. We consider the problem in a fully Bayesian nonparametric framework with Polya tree priors. Our findings are expected to be useful in life testing and survival analysis where Dirichlet process priors are not quite suitable. We derive Bayes factors for some fixed power in the Lehmann alternative and also for the case where the power is treated as a parameter. Our Bayesian solution has a closed form even for censored data. It can be calculated easily and has a ready interpretation.

Key words and phrases: Bayes factor, order statistics, ranks, spacings.