A Bayesian nonparametric testing procedure for paired samples |
| |
Authors: | Luz Adriana Pereira Daniel Taylor-Rodríguez Luis Gutiérrez |
| |
Institution: | 1. Escuela de Estadística, Universidad del Valle, Cali, Colombia;2. Department of Mathematics and Statistics, Portland State University, Portland, Oregon;3. Departamento de Estadística, Pontificia Universidad Católica de Chile, Santiago, Chile |
| |
Abstract: | 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. |
| |
Keywords: | dependent samples Dirichlet process mixture model shift function spike-slab priors |
|
|