A Reference Bayesian Test for Nested Hypotheses and its Relationship to the Schwarz Criterion

References

• Albert , J. H. and Chib , S. 1993 . “Bayesian Analysis of Binary and Polychotomous Response Data,” . Journal of the American Statistical Association , 88 : 669 – 679 .
   Web of Science ®Google Scholar
• Berger , J. O. and Pericchi , L. R. 1993 . “The Intrinsic Bayes Factor for Model Selection and Prediction,” , Purdue University, Dept. of Statistics . Technical Report 93–43C
   Google Scholar
• Berger , J. O. and Pericchi , L. R. “The Intrinsic Bayes Factor for Linear Models,” . The Proceedings of the Fifth Valencia Conference on Bayesian Statistics.
   Google Scholar
• Cox , D. R. and Hinkley , D. V. 1980 . Problems and Solutions in Theoretical Statistics , London : Chapman and Hall .
   Google Scholar
• DiCiccio , T. , Kass , R. , Raftery , A. and Wasserman , L. 1995 . “Computing Bayes Factors by Combining Simulation and Large Sample Approximations,” manuscript in progress
   Google Scholar
• Doob , J. L. “Application of the Theory of Martingales,” . Colloques Internationaux du Centre National de la Recherche Scientifique . Paris . pp. 23 – 27 .
   Google Scholar
• Finney , D. J. 1947 . “The Estimation From Individual Records of the Relationship Between Dose and Quantal Response,” . Biometrika , 34 : 320 – 334 .
   PubMed Web of Science ®Google Scholar
• Hannan , E. J. 1980 . “The Estimation of the Order of an ARMA Process,” . The Annals of Statistics , 8 : 1071 – 1081 .
   Web of Science ®Google Scholar
• Hsiao , C. K. 1994 . “Bayesian Tests of Extra Binomial Variability With Emphasis on the Boundary Case,” , Ph.D. dissertation Carnegie Mellon University, Dept. of Statistics .
   Google Scholar
• Kass , R. E. 1989 . “The Geometry of Asymptotic Inference” . Statistical Science , 4 : 188 – 234 . (with discussion)
   Google Scholar
• Kass , R. E. and Raftery , A. E. 1995 . “Bayes Factors and Model Uncertainty,” . Journal of the American Statistical Association , 90 : 773 – 795 .
   Web of Science ®Google Scholar
• Kass , R. E. , Tierney , L. and Kadane , J. B. 1990 . “The Validity of Posterior Expansions Based on Laplace's Method,” . In Essays in Honor of George Barnard , Edited by: Geisser , S. , Hodges , J. S. , Press , S. J. and Zellner , A. 473 – 488 . Amsterdam : North-Holland .
   Google Scholar
• Kass , R. E. and Vaidyanathan , S. 1992 . “Approximate Bayes Factors and Orthogonal Parameters, With Application to Testing Equality of Two Binomial Proportions,” . Journal of the Royal Statistical Society , 54 : 129 – 144 . Ser. B
   Google Scholar
• Kass , R. and Wasserman , L. 1992 . “Improving the Laplace Approximation Using Posterior Simulation,” , Carnegie Mellon University, Dept. of Statistics . Technical Report 566
   Google Scholar
• Kass , R. and Wasserman , L. 1995a . Comment on O'Hagan's “Fractional Bayes Factors for Model Comparisons,” . Journal of the Royal Statistical Society , 57 : 131 – 132 . Ser. B
   Google Scholar
• Kass , R. and Wasserman , L. Comment on Berger and Pericchi's “The Intrinsic Bayes Factor for Linear Models,” . Proceedings of the Fifth Valencia Conference on Bayesian Statistics.
   Google Scholar
• Kass , R. and Wasserman , L. 1995c . “Formal Rules for Constructing Priors,” . Journal of the American Statistical Association , to appear
   PubMed Web of Science ®Google Scholar
• O'Hagan , A. 1995 . “Fractional Bayes Factors for Model Comparisons,” . Journal of the Royal Statistical Society , 57 : 99 – 138 . Ser. B
   Google Scholar
• Raftery , A. E. 1993 . “Approximate Bayes Factors and Accounting for Model Uncertainty in Generalized Linear Models,” , University of Washington, Dept. of Statistics . Technical Report 255
   Google Scholar
• Raftery , A. E. 1994 . “Hypothesis Testing and Model Selection Via Posterior Simulation,” Edited by: Gilks , W. R. , Spiegelhalter , D. J. and Richardson , S. to appear in Practical Markov Chain Monte Carlo
   Google Scholar
• Schwarz , G. 1978 . “Estimating the Dimension of a Model,” . The Annals of Statistics , 6 : 461 – 464 .
   Web of Science ®Google Scholar
• Smith , A. M. F. and Spiegelhalter , D. J. 1980 . “Bayes Factors and Choice Criteria for Linear Models,” . Journal of the Royal Statistical Society , 42 : 213 – 220 . Ser. B
   Google Scholar
• Stone , M. 1979 . “Comments on Model Selection Criteria of Akaike and Schwarz,” . Journal of the Royal Statistical Society , 41 : 276 – 278 . Ser. B
   Google Scholar
• Zellner , A. and Siow , A. “Posterior Odds Ratios for Selected Regression Hypotheses,” . Bayesian Statistics: Proceedings of the First International Meeting Held in Valencia . Edited by: Bernardo , J. M. , DeGroot , M. H. , Lindley , D. V. and Smith , A. F.M. Valencia : University of Valencia Press .
   Google Scholar