Nothing Special   »   [go: up one dir, main page]

Skip to main content
Log in

On Bayesian model and variable selection using MCMC

  • Published:
Statistics and Computing Aims and scope Submit manuscript

Abstract

Several MCMC methods have been proposed for estimating probabilities of models and associated 'model-averaged' posterior distributions in the presence of model uncertainty. We discuss, compare, develop and illustrate several of these methods, focussing on connections between them.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  • Besag J. 1997. Comment on 'On Bayesian analysis of mixtures with an unknown number of components'. Journal of Royal Statistical Society B 59: p. 774.

    Google Scholar 

  • Carlin B.P. and Chib S. 1995. Bayesian model choice via Markov chain Monte Carlo methods. Journal of Royal Statistical Society B 157: 473-484.

    Google Scholar 

  • Chipman H. 1996. Bayesian variable selection with related predictors.Canadian Journal of Statistics 24: 17-36.

    Google Scholar 

  • Clyde M. and DeSimone-Sasinowska H. 1998. Accounting for model uncertainty in Poisson regression models: Does particulate matter particularly matter? Institute of Statistics and Decision Sciences, Duke University, Technical Report 97-06.

  • Dellaportas P. and Forster J.J. 1999. Markov chain Monte Carlo model determination for hierarchical and graphical log-linear models.Biometrika 86: 615-633.

    Google Scholar 

  • Dellaportas P. and Smith A.F.M. 1993. Bayesian inference for generalised linear and proportional hazards models via Gibbs sampling. Applied Statistics 42: 443-459.

    Google Scholar 

  • George E. and McCulloch R.E. 1993. Variable selection via Gibbs sampling. Journal of the American Statistical Association 88: 881-889.

    Google Scholar 

  • Godsill S.J. 1998. On the relationship between MCMC model uncertainty methods. Signal Processing Group, Cambridge University Engineering Department, Technical Report.

  • Green P. 1995. Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82: 711-732.

    Google Scholar 

  • Green P. and O'Hagan A. 1998. Model choice with MCMC on product spaces without using pseudopriors. Department of Mathematics, University of Nottingham, Technical Report.

  • Gruet M.-A. and Robert C. 1997. Comment on 'On Bayesian analysis of mixtures with an unknown number of components'. Journal of Royal Statistical Society B 59: p. 777.

    Google Scholar 

  • Healy M.J.R. 1988. Glim: An Introduction. Claredon Press, UK.

    Google Scholar 

  • Kuo L. and Mallick B. 1998. Variable selection for regression models.Sankhyā, B 60: 65-81.

    Google Scholar 

  • Madigan D. and York J. 1995. Bayesian graphical models for discrete data. International Statistical Review 63: 215-232.

    Google Scholar 

  • Raftery A.E. 1996. Approximate bayes factors and accounting for model uncertainty in generalised linear models. Biometrika 83: 251-266.

    Google Scholar 

  • Raftery A.E., Madigan D., and Hoeting J.A. 1997. Bayesian model averaging for linear regression models. Journal of the American Statistical Association 92: 179-191.

    Google Scholar 

  • Richardson S. and Green P.J. 1997. On Bayesian analysis of mixtures with an unknown number of components (with discussion).Journal of Royal Statistical Society B 59: 731-792.

    Google Scholar 

  • Roberts G.O. 1996. Markov chain concepts related to sampling algorithms.In: Gilks W.R., Richardson S., and Spiegelhalter D.J.(Eds.), Markov Chain Monte Carlo in Practice. Chapman and Hall, London, pp. 45-57.

    Google Scholar 

  • Tierney L. 1994. Markov chains for exploring posterior distributions (with discussion). Annals of Statistics 22: 1701-1762.

    Google Scholar 

Download references

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dellaportas, P., Forster, J.J. & Ntzoufras, I. On Bayesian model and variable selection using MCMC. Statistics and Computing 12, 27–36 (2002). https://doi.org/10.1023/A:1013164120801

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1013164120801

Navigation