Comparison of Bayesian objective procedures for variable selection in linear regression

Test

Volumn 17, Issue 3, 2008, Pages 472-490

  Moreno, Elías ^a   Girón, F Javier ^b  

^a UNIVERSITY OF GRANADA   (Spain)

^b UNIVERSITY OF MÁLAGA   (Spain)

Author keywords

Encompassing; Intrinsic priors; Linear regression; Model selection; Reference priors

Indexed keywords

EID: 57649184416     PISSN: 11330686     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11749-006-0039-1     Document Type: Article

References (29)

1. AC Atkinson 1978 Posterior probabilities for choosing a regression model Biometrika 65 39 48
2. Berger JO, Bernardo JM (1992) On the development of reference priors (with discussion). In: Bernardo JM, Berger JO Dawid AP, Smith AFM (eds) Bayesian statistics, vol 4. Oxford University Press, Oxford, pp 35-60
3. JO Berger LR Pericchi 1996 The intrinsic Bayes factor for model selection and prediction J Am Stat Assoc 91 109 122
4. JO Berger LR Pericchi 2004 Training samples in objective Bayesian model selection Ann Stat 32 841 869
5. GEP Box RD Meyer 1986 An analysis for unreplicated fractional factorial Technometrics 28 11 18
6. G Casella E Moreno 2005 Intrinsic meta-analysis of contingency tables Stat Med 24 583 604
7. G Casella E Moreno 2006 Objective Bayesian variable selection J Am Stat Assoc 101 157 167
8. M Clyde H Simone G Parmigiani 1996 Prediction via orthogonalized model mixing J Am Stat Assoc 91 1197 1208
9. EI George RE [tmp] McCulloch 1993 Variable selection via Gibbs sampling J Am Stat Assoc 88 881 889
10. George EI, McCulloch RE (1995) Stochastic search variable selection. In: Gilks WR, Richardson S, Spegelhalter DJ (eds) Practical Markov chain Monte Carlo in practice. Chapman and Hall, London, pp 339-348
11. EI George RE [tmp] McCulloch 1997 Approaches for variable selection Stat Sin 7 339 373
12. Geweke J (1996) Variable selection and model comparison in regression. In: Bernardo JM, Berger JO, Dawid AP, Smith AFM (eds) Bayesian statistics, vol 5. Oxford University Press, Oxford, pp 169-194
13. FJ Girón ML Martínez E Moreno F Torres 2006 Objective testing procedures in linear models. Calibration of the p-values Scand J Stat 33 765 784
14. Girón FJ, Moreno E, Martínez ML (2006b) An objective Bayesian procedure for variable selection in regression. In: Balakrishnan N, Castillo E, Sarabia JM (eds) Advances on distribution theory, order statistics and inference. Statistics for industry and technology. Birkhäuser, Boston, pp 393-408
15. I Guttman D Peña D Redondas 2005 A Bayesian approach for predicting with polynomial regression of unknown degree Technometrics 47 23 33
16. Hastie T, Tibshirani R, Friedman J (2001) The elements of statistical learning: data mining, inference and prediction. Springer, New York
17. L Kuo B Mallick 1998 Variable selection for regression models Sankhyā 60 65 81
18. TJ Mitchell JJ Beauchamp 1988 Bayesian variable selection in linear regression (with discussion) J Am Stat Assoc 83 1023 1036
19. E Moreno F Bertolino W Racugno 1998 An intrinsic limiting procedure for model selection and hypotheses testing J Am Stat Assoc 93 1451 1460
20. E Moreno FJ Girón 2005 Consistency of Bayes factors for intrinsic priors in normal linear models Comptes Rendus Math Acad Des Sci Paris 340 11 911 914
21. E Moreno FJ Girón F Torres 2003 Intrinsic priors for hypothesis testing in normal regression models RACSAM Revista R Acad Cienc Exactas Fís Nat Ser A Mat 97 1 53 61
22. CM Morris 1987 Discussion of Casella and Berger J Am Stat Assoc 82 106 111
23. LR Pericchi 1984 An alternative to the standard Bayesian procedure for discrimination between normal linear models Biometrika 71 575 586
24. Poirier DJ (1985) Bayesian hypothesis testing in linear models with continuously induced conjugate prior across hypotheses. In: Bernardo JM, DeGroot MH, Lindley DV, Smith AFM (eds) Bayesian statistics, vol 2. North-Holland, Amsterdam, pp 711-722
25. AFM Smith DJ Spiegelhalter 1980 Bayes factor and choice criteria for linear models J Roy Stat Soc Ser B 42 213 220
26. M Smith R Kohn 1996 Nonparametric regression using Bayesian variable selection J Econom 75 317 344
27. Snedecor J, Cochran W (1982) Statistical methods, 7th edn. Iowa State University Press
28. DJ Spiegelhalter AFM Smith 1982 Bayes factor for linear and log-linear models with vague prior information J Roy Stat Soc Ser B 44 377 387
29. T Stamey J Kabakin J [tmp] McNeal I Johnstone F Freiha E Redwine N Yang 1989 Prostate specific antigen in the diagnosis and treatment of adenocarcinoma of the prostate II: radical prostatectomy treated patients J Urol 16 1076 1083