Objective Bayesian variable selection

Journal of the American Statistical Association

Volumn 101, Issue 473, 2006, Pages 157-167

  Casella, George ^a   Moreno, Elías ^b  

^a University of Florida ^*  (United States)

^b UNIVERSITY OF GRANADA   (Spain)

Author keywords

Intrinsic prior; Metropolis Hastings algorithm; Monte Carlo Markov chain methods; Normal linear regression

Indexed keywords

EID: 33645512673     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/016214505000000646     Document Type: Article

References (35)

1. Atkinson, A. C. (1978), "Posterior Probabilities for Choosing a Regression Model," Biometrika, 65, 39-48.
2. Berger, J. O., and Pericchi, L. R. (1996), "The Intrinsic Bayes Factor for Model Selection and Prediction," Journal of the American Statistical Association, 91, 109-122.
3. _ (1997a), "On the Justification of Default and Intrinsic Bayes Factor," in Modeling and Prediction, eds. J. C. Lee et al., New York: Springer-Verlag, pp. 276-293.
4. _ (1997b), "Accurate and Stable Bayesian Model Selection: The Median Intrinsic Bayes Factor," Sankhyā, Ser. B, 60, 1-18.
5. _ (1998), "On Criticism and Comparison of Default Bayes Factors for Model Selection and Hypothesis Testing," in Proceedings of the Workshop on Model Selection, ed. W. Racugno, Bologna: Pitagora, pp. 1-50.
6. Box, G. E. P., and Meyer, R. D. (1986), "An Analysis for Unreplicated Fractional Factorial," Technometrics, 28, 11-18.
7. Breiman, L. (2001), "Statistical Modeling: The Two Cultures" (with discussion). Statistical Science, 16, 199-231.
8. Breiman, L., and Friedman, J. (1985), "Estimating Optimal Transformations for Multiple Regression and Correlation," Journal of the American Statistical Association, 80, 580-598.
9. Brown, P. J., Vanucci, M., and Fearn, T. (2002), "Bayes Model Averaging With Selection of Regressors," Journal of the Royal Statistical Society, Ser. B, 64, 519-536.
10. Chipman, H., George, E., and McCulloch, R. E. (2001), The Practical Implementation of Bayesian Model Selection, Hayward, CA: IMS, pp. 67-116.
11. Clyde, M. (2001), Discussion of The Practical Implementation of Bayesian Model Selection, by H. Chipman, E. George, and R. E. McCulloch, in Model Selection, Hayward, CA: IMS, pp. 117-124.
12. Clyde, M., DeSimone, H., and Parmigiani, G. (1996), "Prediction via Orthogonalized Model Mixing," Journal of the American Statistical Association, 91, 1197-1208.
13. Draper, N., and Smith, H. (1981), Applied Regression Analysis (2nd ed.), New York: Wiley.
14. George, E. I., and McCulloch, R. E. (1993), "Variable Selection via Gibbs Sampling," Journal of the American Statistical Association, 88, 881-889.
15. _ (1995), "Stochastic Search Variable Selection," in Practical Markov Chain Monte Carlo in Practice, eds. W. R. Gilks et al., London: Chapman & Hall, pp. 339-348.
16. _ (1997), "Approaches for Variable Selection," Statistica Sinica, 1, 339-373.
17. Geweke, J. (1996), "Variable Selection and Model Comparison in Regression," in Bayesian Statistics 5, eds. J. M. Bernardo et al., Oxford University Press, pp. 169-194.
18. Geyer, C. J., and Thompson, E. A. (1995), "Annealing Markov Chain Monte Carlo With Applications to Ancestral Inference," Journal of the American Statistical Association, 90, 909-920.
19. Girón, F. J., Martínez, M. L., Moreno, E., and Torres, F. (2003), "Bayesian Analysis of Matched Pairs in the Presence of Covariates," in Bayesian Statistics 7, eds. J. M. Bernardo et al., Oxford, U.K.: Oxford University Press, pp. 553-563.
20. Jerrum, M., and Sinclair, A. (1996), "The Markov Chain Monte Carlo Method: An Approach to Approximate Counting and Integration," in Approximation Algorithms for NP-Hard Problems, Boston: PWS Publishing, pp. 482-487.
21. Mitchell, T. J., and Beauchamp, J. J. (1988), "Bayesian Variable Selection in Linear Regression" (with discussion), Journal of the American Statistical Association, 83, 1023-1036.
22. 1-Statistical Procedures and Related Topics, ed. D. Yadolah, Hayward, CA: Institute of Mathematical Statistics, pp. 257-270.
23. _ (2005), "Objective Bayesian Analysis for One-Sided Testing," Test, 14, 181-198.
24. Moreno, E., Bertolino, F., and Racugno, W. (1998), "An Intrinsic Limiting Procedure for Model Selection and Hypotheses Testing," Journal of the American Statistical Association, 93, 1451-1460.
25. _ (1999), "Default Bayesian Analysis of the Behrens-Fisher Problem," Journal of Statistical Planning and Inference, 81, 323-333.
26. _ (2000), "Bayesian Model Selection Approach to Analysis of Variance Under Heteroscedasticity," Journal of the Royal Statistical Society, Ser. D, 46, 1-15.
27. Moreno, E., and Liseo, B. (2003), "A Default Bayesian Test for the Number of Components in a Mixture," Journal of Statistical Planning and Inference, 111, 129-142.
28. Moreno, E., Torres, F., and Casella, G. (2005), "Testing Equality of Regression Coefficients in Heteroscedastic Normal Regression Models," Journal of Statistical Planning and Inference, 131, 117-134.
29. Morris, C. N. (1987), Comment on "Testing of a Point Null Hypothesis: The Irreconcilability of Significance Levels and Evidence," by J. O. Berger and T. Sellke; and "Reonciling Bayesian and Frequentist Evidence in the One-Side Testing Problem," by G. Cassella and R. L. Berger, Journal of the American Statistical Association, 82, 106-139.
30. Pericchi, L. R. (1984), "An Alternative to the Standard Bayesian Procedure for Discrimination Between Normal Linear Models," Biometrika, 71, 575-586.
31. Poirier, D. J. (1985), "Bayesian Hypothesis Testing in Linear Models With Continuously Induced Conjugate Prior Across Hypotheses," in Bayesian Statistics 2, eds. J. M. Bernardo et al., New York: Elsevier, pp. 711-722.
32. Smith, M., and Kohn, R. (1996), "Nonparametric Regression Using Bayesian Variable Selection," Journal of Econometrics, 75, 317-344.
33. Smith, A. F. M., and Spiegelhalter, D. J. (1980), "Bayes Factor and Choice Criteria for Linear Models," Journal of the Royal Statistical Society, Ser. B, 42, 213-220.
34. Spiegelhalter, D. J., and Smith, A. F. M. (1982), "Bayes Factor for Linear and Log-Linear Models With Vague Prior Information," Journal of the Royal Statistical Society, Ser. B, 44, 377-387.
35. Wood, H., Steinour, H. H., and Starke, H. R. (1932), "Effect of Composition of Portland Cement on Heat Evolved During Hardening," Industrial and Engineering Chemistry, 24, 1207-1214.