Posterior Cumulant Relationships in Bayesian Inference Involving the Exponential Family

References

• Andrews , D. F. and Herzberg , A. M. 1985 . Data , Berlin : Springer-Verlag .
   Google Scholar
• Barndorff-Nielsen , O. 1978 . Information and Exponential Families in Statistical Theory , New York : John Wiley .
   Google Scholar
• Brown , L. D. 1985 . Foundations of Exponential Families , Hayward , CA : Institute of Mathematical Statistics . IMS Lecture Notes Monograph Series
   Google Scholar
• Dawid , A. P. 1973 . “Posterior Expectations for Large Observations,” . Biometrika , 60 : 664 – 666 .
   Web of Science ®Google Scholar
• Diaconis , P. and Ylvisaker , D. 1979 . “Conjugate Priors for Exponential Families,” . The Annals of Statistics , 7 : 269 – 281 .
   Web of Science ®Google Scholar
• Diaconis , P. and Ylvisaker , D. 1985 . “Quantifying Prior Opinion,” . In Bayesian Statistics 2 , Edited by: Bernardo , J. M. 133 – 156 . Amsterdam : North-Holland .
   Google Scholar
• Goldstein , M. 1977 . “On Contractions of Bayes Estimators for Exponential Family Distributions,” . The Annals of Statistics , 5 : 1235 – 1239 .
   Web of Science ®Google Scholar
• Hill , B. M. 1974 . “On Coherence, Inadmissibility, and Inference About Many Parameters in the Theory of Least Squares,” . In Studies in Bayesian Econometrics and Statistics , Edited by: Fienberg , S. E. and Zellner , A. 555 – 584 . Amsterdam : North-Holland .
   Google Scholar
• Hudson , H. M. 1978 . “A Natural Identity for Exponential Families With Applications in Multivariate Estimation,” . The Annals of Statistics , 6 : 473 – 484 .
   Web of Science ®Google Scholar
• Maritz , J. S. 1970 . Empirical Bayes Methods , London : Methuen .
   Google Scholar
• Masreliez , C. J. 1975 . “Approximate Non-Gaussian Filtering With Linear State and Observation Relations,” . IEEE Transactions on Automatic Control , AC-20 : 107 – 110 .
   Web of Science ®Google Scholar
• Meeden , G. and Isaacson , D. 1977 . “Approximate Behavior of the Posterior Distribution for a Large Observation,” . The Annals of Statistics , 5 : 899 – 908 .
   Web of Science ®Google Scholar
• Miyasawa , K. 1960 . “An Empirical Bayes Estimator of the Mean of a Normal Population,” . Bulletin of the International Statistical Institute , 38 : 181
   Google Scholar
• Naylor , J. C. and Smith , A. F. M. 1982 . “Applications of a Method for the Efficient Computation of Posterior Distributions,” . Applied Statistics , 31 : 214 – 225 .
   Web of Science ®Google Scholar
• O'Hagan , A. 1979 . “On Outlier Rejection Phenomena in Bayes Inference,” . Journal of the Royal Statistical Society , 41 : 358 – 367 . Ser. B
   Google Scholar
• O'Hagan , A. 1981 . “A Moment of Indecision,” . Biometrika , 68 : 329 – 330 .
   Web of Science ®Google Scholar
• Pericchi , L. R. and Smith , A. F. M. 1992 . “Exact and Approximate Posterior Moments for a Normal Location Parameter,” . Journal of the Royal Statistical Society , 54 : 793 – 804 . Ser. B
   Google Scholar
• Poison , N. G. 1991 . “A Representation of the Posterior Mean in a Location Model,” . Biometrika , 78 : 426 – 430 .
   Web of Science ®Google Scholar
• Sampson , A. R. 1975 . “Characterizing Exponential Family Distributions by Moment-Generating Functions,” . The Annals of Statistics , 3 : 747 – 753 .
   Web of Science ®Google Scholar
• Sansó , B. and Perrichi , L. R. 1992 . “Near-Ignorance Classes of Log-Concave Priors for the Location Model,” . TEST: Journal of the Spanish Statistical Society , 1 : 39 – 46 .
   Google Scholar
• Smith , A. F. M. 1983 . “Bayesian Approaches to Outliers and Robustness,” . In Specifying Statistical Models , Edited by: Florens , J. P. 13 – 35 . New York : Springer-Verlag .
   Google Scholar
• West , M. 1981 . “Robust Sequential Approximate Bayesian Estimation,” . Journal of the Royal Statistical Society , 43 : 157 – 166 . Ser. B
   Google Scholar