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Bayesian inference using a noninformative prior for linear Gaussian random coefficient regression with inhomogeneous within-class variances

Author

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  • Clemens Elster

    (Physikalisch-Technische Bundesanstalt (PTB))

  • Gerd Wübbeler

    (Physikalisch-Technische Bundesanstalt (PTB))

Abstract

A Bayesian inference for a linear Gaussian random coefficient regression model with inhomogeneous within-class variances is presented. The model is motivated by an application in metrology, but it may well find interest in other fields. We consider the selection of a noninformative prior for the Bayesian inference to address applications where the available prior knowledge is either vague or shall be ignored. The noninformative prior is derived by applying the Berger and Bernardo reference prior principle with the means of the random coefficients forming the parameters of interest. We show that the resulting posterior is proper and specify conditions for the existence of first and second moments of the marginal posterior. Simulation results are presented which suggest good frequentist properties of the proposed inference. The calibration of sonic nozzle data is considered as an application from metrology. The proposed inference is applied to these data and the results are compared to those obtained by alternative approaches.

Suggested Citation

  • Clemens Elster & Gerd Wübbeler, 2017. "Bayesian inference using a noninformative prior for linear Gaussian random coefficient regression with inhomogeneous within-class variances," Computational Statistics, Springer, vol. 32(1), pages 51-69, March.
    • Handle: RePEc:spr:compst:v:32:y:2017:i:1:d:10.1007_s00180-015-0641-3
    DOI: 10.1007/s00180-015-0641-3
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    References listed on IDEAS

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    1. Foulley, J. L. & San Cristobal, M. & Gianola, D. & Im, S., 1992. "Marginal likelihood and Bayesian approaches to the analysis of heterogeneous residual variances in mixed linear Gaussian models," Computational Statistics & Data Analysis, Elsevier, vol. 13(3), pages 291-305, April.
    2. Miao-Yu Tsai & Chuhsing Hsiao, 2008. "Computation of reference Bayesian inference for variance components in longitudinal studies," Computational Statistics, Springer, vol. 23(4), pages 587-604, October.
    3. Yang, R. Y., 1995. "Bayesian Analysis for Random Coefficient Regression Models Using Noninformative Priors," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 283-311, November.
    4. Wand, M.P., 2007. "Fisher information for generalised linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 98(7), pages 1412-1416, August.
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    Cited by:

    1. Selma Metzner & Gerd Wübbeler & Clemens Elster, 2019. "Approximate large-scale Bayesian spatial modeling with application to quantitative magnetic resonance imaging," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(3), pages 333-355, September.

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