Consistency of Bayesian linear model selection with a growing number of parameters

Journal of Statistical Planning and Inference

Volumn 141, Issue 11, 2011, Pages 3463-3474

  Shang, Zuofeng ^a   Clayton, Murray K ^a  

^a University of Wisconsin   (United States)

Author keywords

Bayesian model selection; Consistency of Bayes factor; Consistency of posterior odds ratio; G priors; Gibbs sampling; Growing number of parameters; Posterior model consistency

Indexed keywords

EID: 79959804064     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2011.05.002     Document Type: Article

References (30)

1. Berger J.O., Pericchi L. The intrinsic Bayes factor for model selection and prediction. J. Amer. Statist. Assoc. 1996, 91:109-122.
2. Berger J.O., Ghosh J.K., Mukhopadhyay N. Approximations and consistency of Bayes factors as model dimension grows. J. Statist. Plann. Inference 2003, 112:241-258.
3. Bühlmann P., Kalisch M., Maathuis M.H. Variable selection in high-dimensional linear models: partially faithful distributions and the PC-simple algorithm. Biometrika 2010, 97:261-278.
4. Casella C., Girón F.J., Martínez M.L., Moreno E. Consistency of Bayesian procedures for variable selection. Ann. Statist. 2009, 37:1207-1228.
5. Clyde M., George E.I. Flexible empirical Bayes estimation for wavelets. J. R. Stat. Soc. Ser. B 2000, 62:681-698.
6. Clyde M., Parmigiani G., Vidakovic B. Multiple shrinkage and subset selection in wavelets. Biometrika 1998, 85:391-401.
7. Durrett R. Probability: Theory and Examples 2005, Wadsworth-Brooks/Cole, Pacific Grove. third ed.
8. Fan J., Lv J. Sure independence screening for ultrahigh dimensional feature space. J. R. Stat. Soc. Ser. B 2008, 70:849-911.
9. Fan J., Peng H. Nonconcave penalized likelihood with a diverging number of parameters. Ann. Statist. 2004, 32:928-961.
10. Fernández C., Ley E., Steel M.F.J. Benchmark priors for Bayesian model averaging. J. Econometrics 2001, 100:381-427.
11. George E., McCulloch R. Variable selection via Gibbs sampling. J. Amer. Statist. Assoc. 1993, 88:881-889.
12. Godsill J.S., Rayner P.J.W. Robust reconstruction and analysis of autoregressive signals in impulsive noise using the Gibbs sampler. IEEE Trans. Speech Audio Process 1998, 6:352-372.
13. Girón F.J., Moreno E., Casella G., Martínez M.L. Consistency of objective Bayes factors for nonnested linear models and increasing model dimension. Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. 2010, 104:57-67.
14. Jeffreys H. Theory of Probability 1967, Oxford University Press, Oxford. fourth ed.
15. Jiang W. Bayesian variable selection for high dimensional generalized linear models: convergence rates of the fitted densities. Ann. Statist. 2007, 35:1487-1511.
16. Liang F., Paulo R., Molina G., Clyde M., Berger J.O. Mixtures of g-priors for Bayesian variable selection. J. Amer. Statist. Assoc. 2008, 103:410-423.
17. Meinshausen N., Bühlmann P. High-dimensional graphs and variable selection with the lasso. Ann. Statist. 2006, 34:1436-1462.
18. Meinshausen N., Yu B. Lasso-type recovery of sparse representations for high-dimensional data. Ann. Statist. 2009, 37:246-270.
19. Moreno E., Bertolino F., Racugno W. An intrinsic limiting procedure for model selection and hypotheses testing. J. Amer. Statist. Assoc. 1998, 93:1451-1460.
20. Moreno E., Girón F.J. Consistency of Bayes factors for intrinsic priors in normal linear models. C. R. Math. Acad. Sci. Paris 2005, 340:911-914.
21. Moreno E., Girón F.J., Casella G. Consistency of objective Bayes factors as the model dimension grows. Ann. Statist. 2010, 38:1937-1952.
22. Shao, J., 2003. Mathematical Statistics, second ed. Springer Texts in Statistics. Springer, New York.
23. Seber G.A.F., Lee A.J. Linear Regression Analysis 2003, Wiley-Interscience, John Wiley & Sons, Hoboken, NJ. second ed.
24. Smith M.S., Kohn R. Nonparametric regression using Bayesian variable selection. J. Econometrics 1996, 75:317-344.
25. Wolfe P.J., Godsill S.J., Ng W.-J. Bayesian variable selection and regularization for time-frequency surface estimation. J. R. Stat. Soc. Ser. B 2004, 66:575-589.
26. Zellner A. An Introduction to Bayesian Inference in Econometrics 1971, Wiley, New York.
27. Zellner A. Jeffreys-Bayes posterior odds ratio and the Akaike information criterion for discriminating between models. Econom. Lett. 1978, 1:337-342.
28. Zellner A. On assessing prior distributions and Bayesian regression analysis with g-prior distributions. Bayesian Inference and Decision Techniques 1986, 233-243. Essays in Honor of Bruno de Finetti, North-Holland/Elsevier. P.K. Goel, A. Zeller (Eds.).
29. Zhang J., Clayton M.K., Townsend P. Functional concurrent linear regression model for spatial images. ournal of Agricultural Biological and Environmental Statistics 2011, 16:105-130.
30. Zhang C.-H., Huang J. The sparsity and bias of the LASSO selection in high-dimensional linear regression. Ann. Statist. 2008, 36:1567-1594.