Nonparametric Bayesian tests

Bayesian methods are ubiquitous in machine learning, bionformatics etc.. Nevertheless, the analysis of empirical results is typically performed by frequentist tests. This implies dealing with null hypothesis significance tests (NHST) and p-values, even though the shortcomings of such methods are well known. We are currently working on the development of nonparametric Bayesian versions of the most used standard frequentist tests (Wilcoxon signed-rank test, Wilcoxon ranksum, Friedman test, etc.) using a Dirichlet process based prior. This research can have an enormous practical impact, since these tests are commonly used in machine learning to compare algorithms performance, in medicine/pharmacology to decide the best among two treatments etc.. Moreover, recently there has been an increasing demand of alternative approaches to NHST. For instance, the journal of Basic and Applied Social Psychology, has banned the use of NHSTs and related statistical procedures from their journal, opening the doors to other approaches.

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