Variable selection via Gibbs sampling

Journal of the American Statistical Association

Volumn 88, Issue 423, 1993, Pages 881-889

  George, Edward I ^a   McCulloch, Robert E ^b  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^b UNIVERSITY OF CHICAGO   (United States)

Author keywords

Data augmentation; Hierarchical Bayes; Latent variables; Mixture; Multiple regression

Indexed keywords

EID: 84893179575     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.1993.10476353     Document Type: Article

References (21)

1. Casella, G., and George, E. I. (1992), “Explaining the Gibbs Sampler,” The American Statistician, 46, 167–174.
2. Diebolt, J., and Robert, C. (in press), “Estimation of Finite Mixture Distributions Through Bayesian Sampling, Journal of the Royal Statistical Society, Ser. B.
3. Draper, N., and Smith, H. (1981), Applied Regression Analysis (2nd ed.), New York: John Wiley.
4. Gelfand, A. E., Hills, S. E., Racine-Poon, A., and Smith, A. F. M. (1990), “Illustration of Bayesian Inference in Normal Data Models Using Gibbs Sampling,” Journal of the American Statistical Association, 85, 972–985.
5. Gelfand, A. E., and Smith, A. F. M. (1990), “Sampling-Based Approaches to Calculating Marginal Densities,” Journal of the American Statistical Association, 85, 398–409.
6. Lempers, F. B. (1971), Posterior Probabilities of Alternative Linear Models, Rotterdam: Rotterdam University Press.
7. Madigan, D., and Raftery, A. E., (1991), “Model Selection and Accounting for Model Uncertainty in Graphical Models Using Occam’s Window,” Technical Report 213, University of Washington, Dept. of Statistics.
8. Miller, A. J. (1990), Subset Selection in Regression, New York: Chapman and Hall.
9. 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.
10. Morris, C. N., (1987), Comment on “The Calculation of Posterior Distributions by Data Augmentation” by M. A. Tanner and W. H. Wong, Journal of the American Statistical Association, 82, 542–543.
11. Pericchi, L. R. (1984), “An Alternative to the Standard Bayesian Procedure for Discrimination Between Normal Linear Models,” Biometrika, 71, 575–586.
12. Poirier, D. J. (1985), “Bayesian Hypothesis Testing in Linear Models With Continuously Induced Conjugate Priors Across Hypotheses,” in Bayesian Statistics 2, eds. J. M. Bernardo, M. H. DeGroot, D. V. Lindley, and A. F. M. Smith, New York: Elsevier, pp. 711–722.
13. Smith, A. F. M., and Spiegelhalter, D. J. (1980), “Bayes Factors and Choice Criteria for Linear Models,” Journal of the Royal Statistical Society, Ser. B, 42, 213–220.
14. Soofi, E. S. (1990), “Effects of Collinearity on Information About Regression Coefficients,” Journal of Econometrics, 43, 255–274.
15. Spiegelhalter, D. J., and Smith, A. F. M. (1982), “Bayes Factors for Linear and Log-Linear Models With Vague Prior Information,” Journal of the Royal Statistical Society, Ser. B, 44, 377–87.
16. Stewart, L. (1987), “Hierarchical Bayesian Analysis Using Monte Carlo Integration: Computing Posterior Distributions When There are Many Possible Models,” The Statistician, 36, 211–219.
17. Tanner, M. A., and Wong, W. H. (1987), “The Calculation of Posterior Distributions by Data Augmentation” (with discussion), Journal of the American Statistical Association, 82, 528–550.
18. Tukey, J. W. (1977), Exploratory Data Analysis, Reading, MA: Addison-Wesley.
19. Verdinelli, I., and Wasserman, L. (1991), “Bayesian Analysis of Outlier Problems Using the Gibbs Sampler,” Statistics and Computing, 1, 105— 117.
20. Zellner, A. (1984), “Posterior Odds Ratios for Regression Hypotheses: General Considerations and Some Specific Results,” in Basic Issues in Econometrics, ed. A. Zellner, Chicago: University of Chicago Press, pp. 275–305.
21. —— (1986), “On Assessing Prior Distributions and Bayesian Regression Analysis with g Prior Distributions,” in Bayesian Inference and Decision Techniques, eds. P. Goel and A. Zellner, New York: Elsevier, pp. 233–243.