IDEAS home Printed from https://ideas.repec.org/a/eee/ecomod/v247y2012icp302-306.html
   My bibliography  Save this article

On model coefficient estimation using Markov chain Monte Carlo simulations: A potential problem and the solution

Author

Listed:
  • Qian, Song S.

Abstract

Markov chain Monte Carlo simulation is increasingly being considered as the tool of choice for model coefficient estimation. In almost all published papers, we use marginal posterior distributions for model coefficients to derive their point estimates, often the marginal means or medians. This note discusses a potential problem of using marginal posterior distribution for deriving point estimates. The problem arises when multiple model coefficients are correlated and the marginal distribution mean or median for each coefficient may not coincide with the respective coefficient value associated with the joint distribution mode. Furthermore, marginal distributions often overestimate model coefficients’ uncertainty. Consequently, we may obtain sub-optimal model coefficient estimates for subsequent inference. This note illustrates this problem through two examples and discusses a likely solution to the problem.

Suggested Citation

  • Qian, Song S., 2012. "On model coefficient estimation using Markov chain Monte Carlo simulations: A potential problem and the solution," Ecological Modelling, Elsevier, vol. 247(C), pages 302-306.
    • Handle: RePEc:eee:ecomod:v:247:y:2012:i:c:p:302-306
    DOI: 10.1016/j.ecolmodel.2012.08.020
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304380012004310
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ecolmodel.2012.08.020?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. Gelman A., 2004. "Parameterization and Bayesian Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 537-545, January.
    Full references (including those not matched with items on IDEAS)

    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. Olawale Awe O. & Adedayo Adepoju A., 2018. "Modified Recursive Bayesian Algorithm For Estimating Time-Varying Parameters In Dynamic Linear Models," Statistics in Transition New Series, Polish Statistical Association, vol. 19(2), pages 258-293, June.
    2. Leonardo Oliveira Martins & Hirohisa Kishino, 2010. "Distribution of distances between topologies and its effect on detection of phylogenetic recombination," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(1), pages 145-159, February.
    3. Matthew Carli & Mary H. Ward & Catherine Metayer & David C. Wheeler, 2022. "Imputation of Below Detection Limit Missing Data in Chemical Mixture Analysis with Bayesian Group Index Regression," IJERPH, MDPI, vol. 19(3), pages 1-17, January.
    4. Breitwieser, Anja & Wick, Katharina, 2016. "What We Miss By Missing Data: Aid Effectiveness Revisited," World Development, Elsevier, vol. 78(C), pages 554-571.
    5. Mingyuan Chen & Dakshina De Silva & Aurelie Slechten, 2021. "Director appointments, boardroom networks, and firm environmental performance," Working Papers 332157256, Lancaster University Management School, Economics Department.
    6. O. Olawale Awe & A. Adedayo Adepoju, 2018. "Modified Recursive Bayesian Algorithm For Estimating Time-Varying Parameters In Dynamic Linear Models," Statistics in Transition New Series, Polish Statistical Association, vol. 19(2), pages 239-258, June.
    7. Anja Breitwieser & Katharina Wick, 2013. "What We Miss By Missing Data: Aid Effectiveness Revisited," Vienna Economics Papers vie1302, University of Vienna, Department of Economics.
    8. Yang, Mingan & Dunson, David B. & Baird, Donna, 2010. "Semiparametric Bayes hierarchical models with mean and variance constraints," Computational Statistics & Data Analysis, Elsevier, vol. 54(9), pages 2172-2186, September.
    9. Faisal Maqbool Zahid & Shahla Faisal & Christian Heumann, 2020. "Variable selection techniques after multiple imputation in high-dimensional data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(3), pages 553-580, September.
    10. Lee, Gyemin & Scott, Clayton, 2012. "EM algorithms for multivariate Gaussian mixture models with truncated and censored data," Computational Statistics & Data Analysis, Elsevier, vol. 56(9), pages 2816-2829.
    11. Breitwieser, Anja & Wick, Katharina, 2016. "What We Miss By Missing Data: Aid Effectiveness Revisited," World Development, Elsevier, vol. 78(C), pages 554-571.
    12. Kuo, Kun-Lin & Wang, Yuchung J., 2018. "Simulating conditionally specified models," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 171-180.
    13. Andrew Gelman, 2004. "Prior distributions for variance parameters in hierarchical models," EERI Research Paper Series EERI_RP_2004_06, Economics and Econometrics Research Institute (EERI), Brussels.
    14. Andrew Gelman, 2004. "Prior distributions for variance parameters in hierarchical models," Econometrics 0404001, University Library of Munich, Germany.
    15. Vinny Davies & Richard Reeve & William T. Harvey & Francois F. Maree & Dirk Husmeier, 2017. "A sparse hierarchical Bayesian model for detecting relevant antigenic sites in virus evolution," Computational Statistics, Springer, vol. 32(3), pages 803-843, September.
    16. Dejing Kong & Lirong Cui, 2016. "Bayesian inference of multi-stage reliability for degradation systems with calibrations," Journal of Risk and Reliability, , vol. 230(1), pages 18-33, February.
    17. Jordan Douglas & Rong Zhang & Remco Bouckaert, 2021. "Adaptive dating and fast proposals: Revisiting the phylogenetic relaxed clock model," PLOS Computational Biology, Public Library of Science, vol. 17(2), pages 1-30, February.

    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:eee:ecomod:v:247:y:2012:i:c:p:302-306. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/ecological-modelling .

    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.