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Gibbs sampler approach for objective Bayesian inference in elliptical multivariate meta-analysis random effects model

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  • Bodnar, Olha
  • Bodnar, Taras

Abstract

Bayesian inference procedures for the parameters of the multivariate random effects model are derived under the assumption of an elliptically contoured distribution when the Berger and Bernardo reference and the Jeffreys priors are assigned to the model parameters. A new numerical algorithm for drawing samples from the posterior distribution is developed, which is based on the hybrid Gibbs sampler. The new approach is compared to the two Metropolis-Hastings algorithms previously derived in the literature via an extensive simulation study. The findings are applied to a Bayesian multivariate meta-analysis, conducted using the results of ten studies on the effectiveness of a treatment for hypertension. The analysis investigates the treatment effects on systolic and diastolic blood pressure. The second empirical illustration deals with measurement data from the CCAUV.V-K1 key comparison, aiming to compare measurement results of sinusoidal linear accelerometers at four frequencies.

Suggested Citation

  • Bodnar, Olha & Bodnar, Taras, 2024. "Gibbs sampler approach for objective Bayesian inference in elliptical multivariate meta-analysis random effects model," Computational Statistics & Data Analysis, Elsevier, vol. 197(C).
    • Handle: RePEc:eee:csdana:v:197:y:2024:i:c:s0167947324000744
    DOI: 10.1016/j.csda.2024.107990
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    References listed on IDEAS

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    1. Norets, Andriy, 2015. "Bayesian regression with nonparametric heteroskedasticity," Journal of Econometrics, Elsevier, vol. 185(2), pages 409-419.
    2. Sundberg,Rolf, 2019. "Statistical Modelling by Exponential Families," Cambridge Books, Cambridge University Press, number 9781108701112, January.
    3. Dungang Liu & Regina Y. Liu & Minge Xie, 2015. "Multivariate Meta-Analysis of Heterogeneous Studies Using Only Summary Statistics: Efficiency and Robustness," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 326-340, March.
    4. Sundberg,Rolf, 2019. "Statistical Modelling by Exponential Families," Cambridge Books, Cambridge University Press, number 9781108476591, January.
    5. Sutradhar, Brajendra C. & Ali, Mir M., 1989. "A generalization of the Wishart distribution for the elliptical model and its moments for the multivariate t model," Journal of Multivariate Analysis, Elsevier, vol. 29(1), pages 155-162, April.
    6. Han Chen & Alisa K. Manning & Josée Dupuis, 2012. "A Method of Moments Estimator for Random Effect Multivariate Meta-Analysis," Biometrics, The International Biometric Society, vol. 68(4), pages 1278-1284, December.
    7. Nicholas G. Polson & James G. Scott & Jesse Windle, 2013. "Bayesian Inference for Logistic Models Using Pólya--Gamma Latent Variables," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(504), pages 1339-1349, December.
    8. William E. Strawderman & Andrew L. Rukhin, 2010. "Simultaneous estimation and reduction of nonconformity in interlaboratory studies," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(2), pages 219-234, March.
    9. Ian R. White, 2011. "Multivariate random-effects meta-regression: Updates to mvmeta," Stata Journal, StataCorp LP, vol. 11(2), pages 255-270, June.
    10. Andrew L. Rukhin, 2013. "Estimating heterogeneity variance in meta-analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(3), pages 451-469, June.
    11. Rukhin, Andrew L., 2007. "Estimating common vector parameters in interlaboratory studies," Journal of Multivariate Analysis, Elsevier, vol. 98(3), pages 435-454, March.
    12. Jian Zhao & Thomas Mathew, 2018. "Some Point Estimates and Confidence Regions for Multivariate Inter-laboratory Data Analysis," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 147-166, December.
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