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.
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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.
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.
Chipman H. 1996. Bayesian variable selection with related predictors.Canadian Journal of Statistics 24: 17-36.
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.
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.
George E. and McCulloch R.E. 1993. Variable selection via Gibbs sampling. Journal of the American Statistical Association 88: 881-889.
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.
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.
Healy M.J.R. 1988. Glim: An Introduction. Claredon Press, UK.
Kuo L. and Mallick B. 1998. Variable selection for regression models.Sankhyā, B 60: 65-81.
Madigan D. and York J. 1995. Bayesian graphical models for discrete data. International Statistical Review 63: 215-232.
Raftery A.E. 1996. Approximate bayes factors and accounting for model uncertainty in generalised linear models. Biometrika 83: 251-266.
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.
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.
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.
Tierney L. 1994. Markov chains for exploring posterior distributions (with discussion). Annals of Statistics 22: 1701-1762.
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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
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DOI: https://doi.org/10.1023/A:1013164120801