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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.

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File URL: http://www.oru.se/PageFiles/15374/wp2007-04.pdf
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Paper provided by Örebro University, School of Business in its series Working Papers with number 2007:4.

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Length: 41 pages
Date of creation: 10 Sep 2007
Date of revision:
Handle: RePEc:hhs:oruesi:2007_004
Contact details of provider: Postal: Örebro University School of Business, SE - 701 82 ÖREBRO, Sweden
Phone: 019-30 30 00
Fax: 019-33 25 46
Web page: http://www.oru.se/Institutioner/Handelshogskolan-vid-Orebro-universitet/

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  1. 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.
  2. Carmen Fernandez & Eduardo Ley & Mark F J Steel, 1998. "Benchmark priors for Bayesian model averaging," ESE Discussion Papers 66, Edinburgh School of Economics, University of Edinburgh.
  3. Smith, M. & Kohn, R., . "Nonparametric Regression using Bayesian Variable Selection," Statistics Working Paper _009, Australian Graduate School of Management.
  4. 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.
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