The intrinsic bayes factor for model selection and prediction

Journal of the American Statistical Association

Volumn 91, Issue 433, 1996, Pages 109-122

  Berger, James O ^a   Pericchi, Luis R ^b  

^a PURDUE UNIVERSITY   (United States)

^b UNIVERSIDAD SIMÓN BOLÍVAR   (Venezuela)

Author keywords

Asymptotic Bayes factors; Hypothesis testing; Noninformative prior; Posterior probability; Training sample

Indexed keywords

EID: 0000298252     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.1996.10476668     Document Type: Article

References (48)

1. Aitkin, M. (1991), “Posterior Bayes Factors,” Journal of the Royal Statistical Society, Ser. B, 53, 111-142.
2. Albert, J. H. (1990), “A Bayesian Test for a Two-Way Contingency Table Using Independence Priors,” Canadian Journal of Statistics, 14, 1583-1590.
3. Atkinson, A. C. (1978), “Posterior Probabilities for Choosing a Regression Model,” Biometrika, 65, 39-48.
4. Berger, J., and Bernardo, J. M. (1992), “On the Development of the Reference Prior Method,” in Bayesian Statistics IV, eds. J. M. Bernardo et al., London: Oxford University Press, pp. 35-60.
5. Berger, J., and Delampady, M. (1987), “Testing Precise Hypotheses,” Statistical Science, 3, 317-352.
6. Berger, J., and Pericchi, L. (1993), “The Intrinsic Bayes Factor for Model Selection and Prediction,” Technical Report 93-43C, Purdue University, Dept, of Statistics.
7. Berger, J., and Pericchi, L. (1994), “The Intrinsic Bayes Factor for Linear Models,” Technical Report 94-10C, Purdue University, Dept, of Statistics.
8. Berger, J., and Pericchi, L. (1995), “The Intrinsic Bayes Factor for Linear Models,” in Bayesian Statistics V, eds. J. M. Bernardo et al., London: Oxford University Press, pp. 23-42.
9. Berger, J., Pericchi, L., and Varshavsky, J. (1995), “An Identity for Linear and Invariant Models, With Application to Non-Gaussian Model Selec-tion,” Technical Report 95-7C, Purdue University, Dept, of Statistics.
10. Berger, J., and Sellke, T. (1987), “Testing a Point Null Hypothesis: The Irreconcilability of P-Values and Evidence,” Journal of the American Statistical Association, 82, 112-122.
11. Bernardo, J. M. (1979), “Reference Posterior Distributions for Bayesian Inference,” Journal of the Royal Statistical Society, Ser. B, 41, 113-147.
12. Chib, S. (1995), “Marginal Likelihood From the Gibbs Output,” to appear in Journal of the American Statistical Association.
13. Delampady, M., and Berger, J. O. (1990), “Lower Bounds on Bayes Factors for Multinomial Distribution, With Application to Chi-Squared Tests of Fit,” The Annals of Statistics, 18, 1295-1316.
14. de Vos, A. F. (1993), “A Fair Comparison Between Regression Models of Different Dimension,” technical report, The Free University, Amsterdam.
15. Dey, D. K. (1995), Discussion of “The Intrinsic Bayes Factor for Linear Models,” by J. Berger and L. Pericchi, in Bayesian Statistics V, eds. J. M. Bernardo et al., London: Oxford University Press, pp. 43-45.
16. Dmochowski, J. (1994), “Intrinsic Priors Via Kullback-Leibler Geometry,” Technical Report 94-15, Purdue University, Dept, of Statistics.
17. Draper, D. (1995), “Assessment and Propagation of Model Uncertainty,” Journal of the Royal Statistical Society, Ser. B, 57, 45-98.
18. Edwards, W., Lindman, H., and Savage, L. J. (1963), “Bayesian Statistical Inference for Psychological Research,” Psychological Review, 70, 193-242.
19. Geisser, S., and Eddy, W. F. (1979), “A Predictive Approach to Model Selection,” Journal of the American Statistical Association, 74, 153-160.
20. Gelfand, A. E., and Dey, D. K. (1994), “Bayesian Model Choice: Asymptotics and Exact Calculations,” Journal of the Royal Statistical Society, Ser. B, 56, 501-514.
21. Gelfand, A. E., Dey, D. K., and Chang, H. (1992), “Model Determination Using Predictive Distributions With Implementations Via Sampling- Based Methods,” (with discussion), in Bayesian Statistics 4, eds. J. M. Bernardo et al., London: Oxford University Press, pp. 147-167.
22. Geyer, C., and Thompson, E. (1992), “Constrained Monte Carlo Maximum Likelihood for Dependent Data,” Journal of the Royal Statistical Society, Ser. B, 54, 657-683.
23. George, E. I., and McCulloch, R. E. (1993), “Variable Selection Via Gibbs Sampling,” Journal of the American Statistical Association, 88, 881-889.
24. Good, I. J. (1985), “Weight of Evidence: A Brief Survey,” in Bayesian Statistics 2, eds. J. M. Bernardo et al., New York: Elsevier, pp. 249-269.
25. Haughton, D. (1988), “On the Choice of a Model to Fit Data From an Exponential Family,” The Annals of Statistics, 16, 342-355.
26. Haughton, D., and Dudley, R. (1992), “Information Criteria for Multiple Data Sets and Restricted Parameters,” technical report, Bentley College, Dept, of Mathematics.
27. Jefferys, W., and Berger, J. (1992), “Ockham's razor and Bayesian analysis,” American Scientist, 80, 64-72.
28. Jeffreys, H. (1961), Theory of Probability, London: Oxford University Press.
29. Kass, R. E., and Raftery, A. (1995), “Bayes Factors,” Journal of the American Statistical Association, 90, 773-795.
30. Kass, R. E., and Wasserman, L. (1995), “A Reference Bayesian Test for Nested Hypotheses and Its Relationship to the Schwarz Criterion,” Jour-nal of the American Statistical Association, 90, 928-934.
31. Lempers, F. B. (1971), Posterior Probabilities of Alternative Linear Models, Rotterdam: University of Rotterdam Press.
32. Madigan, D., and Raftery, A. E. (1994), “Model Selection and Accounting for Model Uncertainty In Graphical Models Using Occam's Window,” Journal of the American Statistical Association, 89, 1535-1546.
33. McCulloch, R. E., and Rossi, P. E. (1993), “Bayes Factors for Nonlinear Hypotheses and Likelihood Distributions,” Biometrika, 79, 663-676.
34. Mitchell, T. J., and Beauchamp, J. J. (1988), “Bayesian Variable Selection in Regression,” Journal of the American Statistical Association, 83, 1023-1032.
35. O'Hagan, A. (1995), “Fractional Bayes Factors for Model Comparisons,” Journal of the Royal Statistical Society, Ser. B, 57, 99-138.
36. Pericchi, L. R., and Pérez, M. E. (1994), “Posterior Robustness With More Than One Sampling Model,” Journal of Statistical Planning and Infer-ence, 40, 279-294.
37. 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 et al., New York: Elsevier, pp. 711-722.
38. Proschan, F. (1963), 'Theoretical Explanation of Observed Decreasing Failure Rate,” Technometrics, 5, 375-383.
39. Raftery, A. E. (1993), “Approximate Bayes Factors and Accounting for Model Uncertainty in Generalized Linear Models,” Technical Report 255, University of Washington, Dept, of Statistics.
40. Rosenkrantz, S. (1992), “The Bayes Factor for Model Evaluation in a Hierarchical Poisson Model for Area Counts,” Ph.D. dissertation, University of Washington, Dept, of Biostatistics.
41. San Martini, A., and Spezzaferri, F. (1984), “A Predictive Model Selection Criterion,” The Journal of the Royal Statistical Society, Ser. B, 46, 296-303.
42. Schwarz, G. (1978), “Estimating the Dimension of a Model,” The Annals of Statistics, 6, 461-464.
43. 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.
44. Spiegelhalter, D. J. (1980), “An Omnibus Test for Normality for Small Samples,” Biometrika, 67, 493-496.
45. 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, 377-387.
46. Stewart, L. (1987), “Hierarchical Bayesian Analysis Using Monte Carlo Integration: Computing Posterior Distributions When There are Many Possible Models,” The Statistician, 36, 211-219.
47. Verdinelli, I., and Wasserman, L. (1995), “Bayes Factors, Nuisance Parameters, and Imprecise Tests,” in Bayesian Statistics V, eds. J. M. Bernardo et al., London: Oxford University Press.
48. Zellner, A., and Siow (1980), “Posterior Odds for Selected Regression Hypotheses,” in Bayesian Statistics 1, eds. J. M. Bernardo et al., Valencia: Valencia University Press, pp. 585-603.