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Theory and Method

Lower Bounds on Bayes Factors for Interval Null Hypotheses

Pages 120-124 | Received 01 Feb 1987, Published online: 12 Mar 2012

References

  • Berger , J. 1985 . Statistical Decision Theory and Bayesian Analysis, , 2nd ed. , New York : Springer-Verlag .
  • Berger , J. and Delampady , M. 1987 . “Bayesian Testing of Precise Hypotheses” . Statistical Science , 2 : 317 – 348 . (with discussion)
  • Berger , J. and Sellke , T. 1987 . “Testing a Point Null Hypothesis: The Irreconcilability of Significance Levels and Evidence,” . Journal of the American Statistical Association , 82 : 112 – 122 .
  • Bernardo , J. M. 1980 . “A Bayesian Analysis of Classical Hypothesis Testing,” . In Bayesian Statistics , Edited by: Bernardo , J. M. , DeGroot , M. H. , Lindley , D. V. and Smith , A. F. M. 605 – 618 . Valencia , , Spain : Valencia University Press .
  • Casella , G. and Berger , R. L. 1987 . “Reconciling Bayesian and Frequentist Evidence in the One-Sided Testing Problem,” . Journal of the American Statistical Association , 82 : 106 – 111 .
  • DeGroot , M. H. 1973 . “Doing What Comes Naturally: Interpreting a Tail Area as a Posterior Probability or as a Likelihood Ratio,” . Journal of the American Statistical Association , 68 : 966 – 969 .
  • Delampady , M. 1986 . “Testing a Precise Hypothesis: Interpreting P-Values From a Robust Bayesian Viewpoint,” , Purdue University, Dept. of Statistics . unpublished Ph.D. thesis
  • Delampady , M. 1987 . “A Robustness Analysis: Credible Regions and Hypothesis Test for Elliptical Distributions,” , University of British Columbia, Dept. of Statistics . Technical Report 55
  • Delampady , M. 1988 . “Lower Bounds on Bayes Factors for Interval Null Hypotheses and Applications to Normal and Student's t Tests,” , University of British Columbia, Dept. of Statistics . Technical Report 62
  • Delampady , M. “Lower Bounds on Bayes Factors for Invariant Testing Situations,” . Journal of Multivariate Analysis , 30 (in press)
  • Delampady , M. and Berger , J. 1987 . “Lower Bounds on Bayes Factors for Multinomial and Chi-Squared Test of Fit,” , University of British Columbia, Dept. of Statistics . Technical Report 53
  • Dempster , A. P. “The Direct Use of Likelihood for Significance Testing,” . Proceedings of the Conference on Foundational Questions in Statistical Inference . Edited by: Barndorff-Nielsen , O. pp. 335 – 352 . Aarhus , , Denmark : University of Aarhus (Dept. of Theoretical Statistics) .
  • Diamond , G. A. and Forrester , J. S. 1983 . “Clinical Trials and Statistical Verdicts: Probable Grounds for Appeal,” . Annals of Internal Medicine , 98 : 385 – 394 .
  • Dickey , J. M. 1971 . “The Weighted Likelihood Ratio, Linear Hypotheses on Normal Location Parameters,” . The Annals of Mathematical Statistics , 42 : 204 – 223 .
  • Dickey , J. M. 1977 . “Is the Tail Area Useful as an Approximate Bayes Factor?” . Journal of the American Statistical Association , 72 : 138 – 142 .
  • Edwards , W. , Lindman , H. and Savage , L. J. 1963 . “Bayesian Statistical Inference for Psychological Research,” . Psychological Review , 70 : 193 – 242 .
  • Good , I. J. 1950 . Probability and the Weighing of Evidence , London : Charles W. Griffin .
  • Good , I. J. 1965 . The Estimation of Probabilities: An Essay on Modern Bayesian Methods , Cambridge , MA : MIT Press .
  • Good , I. J. 1967 . “A Bayesian Significance Test for the Multinomial Distribution,” . Journal of the Royal Statistical Society , 29 : 399 – 431 . Ser. B
  • Hildreth , C. 1963 . “Bayesian Statisticians and Remote Clients,” . Econometrica , 31 : 422 – 438 .
  • Jeffreys , H. 1961 . Theory of Probability, , 3rd ed. , Oxford , , U.K. : Oxford University Press .
  • Lempers , F. B. 1971 . Posterior Probabilities of Alternative Models , Rotterdam : University of Rotterdam Press .
  • Lindley , D. V. 1957 . “A Statistical Paradox,” . Biometrika , 44 : 187 – 192 .
  • Pratt , J. W. 1965 . “Bayesian Interpretation of Standard Inference Statements” . Journal of the Royal Statistical Society , 27 : 169 – 203 . (with discussion), Ser. B
  • Smith , A. F. M. and Spiegelhalter , D. J. 1980 . “Bayes Factors and Choice Criteria for Linear Models,” . Journal of the Royal Statistical Society , 42 : 213 – 220 . Ser. B
  • Zellner , A. 1984 . “Posterior Odds Ratios for Regression Hypotheses: General Considerations and Some Specific Results,” . In Basic Issues in Econometrics , Chicago : University of Chicago Press .

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