Advanced Search
MyIDEAS: Login to save this article or follow this journal

On efficient calculations for Bayesian variable selection

Contents:

Author Info

  • Ruggieri, Eric
  • Lawrence, Charles E.
Registered author(s):

    Abstract

    We describe an efficient, exact Bayesian algorithm applicable to both variable selection and model averaging problems. A fully Bayesian approach provides a more complete characterization of the posterior ensemble of possible sub-models, but presents a computational challenge as the number of candidate variables increases. While several approximation techniques have been developed to deal with problems that contain a large numbers of candidate variables, including BMA, IBMA, MCMC and Gibbs Sampling approaches, here we focus on improving the time complexity of exact inference using a recursive algorithm (Exact Bayesian Inference in Regression, or EBIR) that uses components of one sub-model to rapidly generate another and prove that its time complexity is O(m2), where m is the number candidate variables. Testing against simulated data shows that EBIR significantly reduces compute time without sacrificing accuracy, while comparisons to the results obtained by MCMC approaches on the Crime and Punishment data set show that model averaging yields improved predictive performance over two model selection approaches. In addition, we show that finite mixtures of centroid solutions provide a means to better characterize the shape of multimodal posterior spaces than any individual model. Finally, we describe how the BIC approximations employed in the BMA and IBMA algorithms can be replaced by an EBIR calculation of equal time complexity and illustrate the departure of the BIC approximation from the exact Bayesian inference of EBIR.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL: http://www.sciencedirect.com/science/article/pii/S0167947311003574
    Download Restriction: Full text for ScienceDirect subscribers only.

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 56 (2012)
    Issue (Month): 6 ()
    Pages: 1319-1332

    as in new window
    Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:1319-1332

    Contact details of provider:
    Web page: http://www.elsevier.com/locate/csda

    Related research

    Keywords: Bayesian model averaging; Variable selection; Dynamic programming; Inversion of matrix sums; Regression; Spike and slab;

    References

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
    as in new window
    1. Gary S. Becker, 1974. "Crime and Punishment: An Economic Approach," NBER Chapters, in: Essays in the Economics of Crime and Punishment, pages 1-54 National Bureau of Economic Research, Inc.
    2. Ehrlich, Isaac, 1975. "The Deterrent Effect of Capital Punishment: A Question of Life and Death," American Economic Review, American Economic Association, vol. 65(3), pages 397-417, June.
    3. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320.
    4. Carmen Fernandez & Eduardo Ley & Mark Steel, 1999. "Model uncertainty in cross-country growth regressions," Econometrics 9903003, EconWPA, revised 06 Oct 2001.
    5. Chris Hans, 2009. "Bayesian lasso regression," Biometrika, Biometrika Trust, vol. 96(4), pages 835-845.
    6. Smith, Michael & Kohn, Robert, 1996. "Nonparametric regression using Bayesian variable selection," Journal of Econometrics, Elsevier, vol. 75(2), pages 317-343, December.
    7. Carmen Fernandez & E Ley & Mark F J Steel, 2004. "Benchmark priors for Bayesian models averaging," ESE Discussion Papers 66, Edinburgh School of Economics, University of Edinburgh.
    8. Jianqing Fan & Jinchi Lv, 2008. "Sure independence screening for ultrahigh dimensional feature space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 849-911.
    9. Theo Eicher & Chris Papageorgiou & Oliver Röhn, 2007. "Unraveling the Fortunates of the Fortunate: An Iterative Bayesian Model Averaging (IBMA) Approach," CESifo Working Paper Series 1907, CESifo Group Munich.
    10. S. Illeris & G. Akehurst, 2001. "Introduction," The Service Industries Journal, Taylor & Francis Journals, vol. 21(1), pages 1-4, January.
    11. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    12. Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
    13. Wang, Hansheng, 2009. "Forward Regression for Ultra-High Dimensional Variable Screening," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1512-1524.
    14. Jiahua Chen & Zehua Chen, 2008. "Extended Bayesian information criteria for model selection with large model spaces," Biometrika, Biometrika Trust, vol. 95(3), pages 759-771.
    15. Ehrlich, Isaac, 1973. "Participation in Illegitimate Activities: A Theoretical and Empirical Investigation," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 521-65, May-June.
    16. Stigler, George J, 1970. "The Optimum Enforcement of Laws," Journal of Political Economy, University of Chicago Press, vol. 78(3), pages 526-36, May-June.
    17. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    18. Efron, Bradley, 2004. "Large-Scale Simultaneous Hypothesis Testing: The Choice of a Null Hypothesis," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 96-104, January.
    19. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768.
    Full references (including those not matched with items on IDEAS)

    Citations

    Lists

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    Statistics

    Access and download statistics

    Corrections

    When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:1319-1332. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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