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A Bayesian nonparametric testing procedure for paired samples

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  • Luz Adriana Pereira
  • Daniel Taylor‐Rodríguez
  • Luis Gutiérrez

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.

Suggested Citation

  • Luz Adriana Pereira & Daniel Taylor‐Rodríguez & Luis Gutiérrez, 2020. "A Bayesian nonparametric testing procedure for paired samples," Biometrics, The International Biometric Society, vol. 76(4), pages 1133-1146, December.
    • Handle: RePEc:bla:biomet:v:76:y:2020:i:4:p:1133-1146
    DOI: 10.1111/biom.13234
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    References listed on IDEAS

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    1. Cipolli III, William & Hanson, Timothy & McLain, Alexander C., 2016. "Bayesian nonparametric multiple testing," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 64-79.
    2. Smith, Michael & Kohn, Robert, 1996. "Nonparametric regression using Bayesian variable selection," Journal of Econometrics, Elsevier, vol. 75(2), pages 317-343, December.
    3. Bhattacharya, Abhishek & Dunson, David, 2012. "Nonparametric Bayes classification and hypothesis testing on manifolds," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 1-19.
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    Cited by:

    1. Ryan Thompson & Catherine S. Forbes & Steven N. MacEachern & Mario Peruggia, 2022. "Familial Inference," Monash Econometrics and Business Statistics Working Papers 2/22, Monash University, Department of Econometrics and Business Statistics.
    2. Pereira, Luz Adriana & Gutiérrez, Luis & Taylor-Rodríguez, Daniel & Mena, Ramsés H., 2023. "Bayesian nonparametric hypothesis testing for longitudinal data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    3. Wyłupek, Grzegorz, 2023. "A nonparametric test for paired data," Journal of Multivariate Analysis, Elsevier, vol. 198(C).

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