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Computational Efficiency in Bayesian Model and Variable Selection


  • Eklund, Jana

    () (Department of Business, Economics, Statistics and Informatics)

  • Karlsson, Sune

    () (Department of Business, Economics, Statistics and Informatics)


Large scale Bayesian model averaging and variable selection exercises present, despite the great increase in desktop computing power, considerable computational challenges. Due to the large scale it is impossible to evaluate all possible models and estimates of posterior probabilities are instead obtained from stochastic (MCMC) schemes designed to converge on the posterior distribution over the model space. While this frees us from the requirement of evaluating all possible models the computational effort is still substantial and efficient implementation is vital. Efficient implementation is concerned with two issues: the efficiency of the MCMC algorithm itself and efficient computation of the quantities needed to obtain a draw from the MCMC algorithm. We evaluate several different MCMC algorithms and find that relatively simple algorithms with local moves perform competitively except possibly when the data is highly collinear. For the second aspect, efficient computation within the sampler, we focus on the important case of linear models where the computations essentially reduce to least squares calculations. Least squares solvers that update a previous model estimate are appealing when the MCMC algorithm makes local moves and we find that the Cholesky update is both fast and accurate.

Suggested Citation

  • Eklund, Jana & Karlsson, Sune, 2007. "Computational Efficiency in Bayesian Model and Variable Selection," Working Papers 2007:4, Örebro University, School of Business.
  • Handle: RePEc:hhs:oruesi:2007_004

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    References listed on IDEAS

    1. Fernandez, Carmen & Ley, Eduardo & Steel, Mark F. J., 2001. "Benchmark priors for Bayesian model averaging," Journal of Econometrics, Elsevier, vol. 100(2), pages 381-427, February.
    2. Smith, Michael & Kohn, Robert, 1996. "Nonparametric regression using Bayesian variable selection," Journal of Econometrics, Elsevier, vol. 75(2), pages 317-343, December.
    3. Gary Koop & Simon Potter, 2004. "Forecasting in dynamic factor models using Bayesian model averaging," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 550-565, December.
    4. Sune Karlsson & Tor Jacobson, 2004. "Finding good predictors for inflation: a Bayesian model averaging approach," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(7), pages 479-496.
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    Cited by:

    1. Jesús Crespo Cuaresma & Gernot Doppelhofer & Martin Feldkircher, 2014. "The Determinants of Economic Growth in European Regions," Regional Studies, Taylor & Francis Journals, vol. 48(1), pages 44-67, January.

    More about this item


    Bayesian Model Averaging; Sweep operator; Cholesky decomposition; QR decomposition; Swendsen-Wang algorithm;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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