IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v32y2017i1d10.1007_s00180-015-0641-3.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-015-0641-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s00180-015-0641-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. G. Kauermann & J. Ormerod & M. Wand, 2010. "Parsimonious Classification Via Generalized Linear Mixed Models," Journal of Classification, Springer;The Classification Society, vol. 27(1), pages 89-110, March.
    2. Pedro Delicado & Juan Romo, 1999. "Goodness of Fit Tests in Random Coefficient Regression Models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(1), pages 125-148, March.
    3. M. A. Alkhamisi & Ghazi Shukur, 2005. "Bayesian analysis of a linear mixed model with AR(p) errors via MCMC," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(7), pages 741-755.
    4. Tang, Min & Slud, Eric V. & Pfeiffer, Ruth M., 2014. "Goodness of fit tests for linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 176-193.
    5. Gwowen Shieh & Jack Lee, 2002. "Bayesian Prediction Analysis for Growth Curve Model Using Noninformative Priors," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(2), pages 324-337, June.
    6. M. C. Pardo & R. Alonso, 2012. "A generalized Q--Q plot for longitudinal data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(11), pages 2349-2362, July.
    7. Miao-Yu Tsai, 2010. "Extended Bayesian model averaging for heritability in twin studies," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(6), pages 1043-1058.
    8. Natarajan, Ranjini, 2001. "On the propriety of a modified Jeffreys's prior for variance components in binary random effects models," Statistics & Probability Letters, Elsevier, vol. 51(4), pages 409-414, February.
    9. Marot, Guillemette & Foulley, Jean-Louis & Jaffrzic, Florence, 2009. "A structural mixed model to shrink covariance matrices for time-course differential gene expression studies," Computational Statistics & Data Analysis, Elsevier, vol. 53(5), pages 1630-1638, March.
    10. Se Yoon Lee, 2022. "Bayesian Nonlinear Models for Repeated Measurement Data: An Overview, Implementation, and Applications," Mathematics, MDPI, vol. 10(6), pages 1-51, March.
    11. Russell D. Wolfinger & Robert E. Kass, 2000. "Nonconjugate Bayesian Analysis of Variance Component Models," Biometrics, The International Biometric Society, vol. 56(3), pages 768-774, September.
    12. Cavicchioli, Maddalena, 2017. "Asymptotic Fisher information matrix of Markov switching VARMA models," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 124-135.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:compst:v:32:y:2017:i:1:d:10.1007_s00180-015-0641-3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.