A Bayesian Nonparametric Testing Procedure for Paired Samples
The work of the first author was supported by CONICYT PFCHA/DOCTORADO BECAS CHILE/2015‐21151465 and “Millenium Nucleus Center for the Discovery of Structures in Complex Data.” The second author was partially supported by NSF 1253225 sub‐award through Michigan State University and NIH 5P30AG024978‐15 sub‐award through OHSU‐ORCATECH. The work of the third author was supported by “Proyecto REDES ETAPA INICIAL, Convocatoria 2017 REDI170094,” and Millennium Science Initiative of the Ministry of Economy, Development, and Tourism, grant “Millenium Nucleus Center for the Discovery of Structures in Complex Data.”
We propose a Bayesian hypothesis testing procedure for comparing the distributions of paired samples. The procedure is based on a flexible model for the joint distribution of both samples. The flexibility is given by a mixture of Dirichlet processes. Our proposal uses a spike‐slab prior specification for the base measure of the Dirichlet process and a particular parametrization for the kernel of the mixture in order to facilitate comparisons and posterior inference. The joint model allows us to derive the marginal distributions and test whether they differ or not. The procedure exploits the correlation between samples, relaxes the parametric assumptions, and detects possible differences throughout the entire distributions. A Monte Carlo simulation study comparing the performance of this strategy to other traditional alternatives is provided. Finally, we apply the proposed approach to spirometry data collected in the United States to investigate changes in pulmonary function in children and adolescents in response to air polluting factors.
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Pereira, L. A., Taylor-Rodríguez, D., & Gutiérrez, L. (2020). A Bayesian nonparametric testing procedure for paired samples. Biometrics. https://doi.org/10.1111/biom.13234