The work of the first author was supported by grants Fondecyt 11140013, ‘Proyecto REDES ETAPA INICIAL, Convocatoria 2017 REDI170094’ and Iniciativa Cient´ıfica Milenio – Minecon N´ucleo Milenio MiDaS. The second author was supported by grants from the National Science Foundation (ACI 1443014 and SES 1131897) and the Alfred P. Sloan Foundation (G-2-15- 20166003). The third author acknowledges partial support of the grant Fondecyt 1150233 and ‘Proyecto REDES ETAPA INICIAL, Convocatoria 2017 REDI170094’. The authors thank the comments from the two referees and the associate editor, which contributed to improving the quality of the manuscript.
Bayes Factor, Dependent Dirichlet Process, Bayesian statistical decision theory
We propose a Bayesian nonparametric strategy to test for differences between a control group and several treatment regimes. Most of the existing tests for this type of comparison are based on the differences between location parameters. In contrast, our approach identifies differences across the entire distribution, avoids strong modeling assumptions over the distributions for each treatment, and accounts for multiple testing through the prior distribution on the space of hypotheses. The proposal is compared to other commonly used hypothesis testing procedures under simulated scenarios. Two real applications are also analyzed with the proposed methodology.
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Gutiérrez, Luis; Barrientos, Andrés F.; González, Jorge; Taylor-Rodríguez, Daniel. A Bayesian Nonparametric Multiple Testing Procedure for Comparing Several Treatments Against a Control. Bayesian Anal. 14 (2019), no. 2, 649--675
Supplementary Material for ‘A Bayesian nonparametric multiple testing procedure for comparing several treatments against a control’. The online Supplementary Material contains the Gibbs Algorithm described in Section 3.4, as well as the image plots of the comparison between our proposal and other classical hypothesis tests (Section 4.2), including both multiple and two-sample cases.