30
Views
7
CrossRef citations to date
0
Altmetric
Theory and Method

Conjugate Parameterizations for Natural Exponential Families

&
Pages 1347-1356 | Received 01 Feb 1994, Published online: 27 Feb 2012

References

  • Albert , J. H. 1989 . “On the Use of Power Transformations to Simplify Posterior Distributions,” , Bowling Green State University, Dept. of Mathematics and Statistics . technical report
  • Barndorff-Nielsen , O. 1978 . Information and Exponential Families in Statistical Theory , Chichester , , UK : John Wiley .
  • Bernardo , J. M. and Smith , A. F. M. 1994 . Bayesian Theory , Chichester , , UK : John Wiley .
  • Casalis , M. 1991 . “Les Families Exponentielles à Variance Quadratique Homogène sont des lois de Wishart sur un Cône Symétrique,” . Comptes Rendus de l'Academie des Sciences, Paris , t. 312 ( I ) : 537 – 540 .
  • Casalis , M. 1994a . “Les 2n + 4 Types de Families Exponentielles Naturelles sur ℝn à Fonction-Variance Quadratique Simple,” . Comptes Rendus de l'Academie des Sciences, Paris , t. 318 ( I ) : 261 – 264 .
  • Casalis , M. 1994b . “The 2d + 4 Simple Quadratic Natural Exponential Families on ℝd,” , Paul Sabatier University, Laboratory of Probability and Statistics . unpublished technical report
  • Consonni , G. and Veronese , P. 1992 . “Conjugate Priors for Exponential Families Having Quadratic Variance Functions,” . Journal of the American Statistical Association , 87 : 1123 – 1127 .
  • Diaconis , P. and Ylvisaker , D. 1979 . “Conjugate Priors for Exponential Families,” . The Annals of Statistics , 7 : 269 – 281 .
  • Diaconis , P. and Ylvisaker , D. 1985 . “Quantifying Prior Opinion,” . In Bayesian Statistics 2 , Edited by: Bernardo , J. M. , DeGroot , M. H. , Lindley , D. V. and Smith , A. F.M. 133 – 156 . Amsterdam : North-Holland .
  • Gutiérrez-Peña , E. 1992 . “Expected Logarithmic Divergence for Exponential Families,” . In Bayesian Statistics 4 , Edited by: Bernardo , J. M. , Berger , J. O. , Dawid , A. P. and Smith , A. F.M. 669 – 674 . Oxford , , UK : Oxford University Press .
  • Hills , S. E. and Smith , A. F. M. 1992 . “Parameterization Issues in Bayesian Inference,” . In Bayesian Statistics 4 , Edited by: Bernardo , J. M. , Berger , J. O. , Dawid , A. P. and Smith , A. F.M. 227 – 246 . Oxford , , UK : Oxford University Press .
  • Jeffreys , H. 1961 . Theory of Probability, , 3rd ed. , Oxford , , UK : Oxford University Press .
  • Letac , G. “The Classification of the Natural Exponential Families by Their Variance Functions,” . Proceedings of the 48th Session of the International Statistical Institute . Vol. 54 , pp. 1 – 18 .
  • Magnus , J. R. and Neudecker , H. 1988 . Matrix Differential Calculus, with Applications in Statistics and Econometrics , Chichester , , UK : John Wiley .
  • Morris , C. N. 1982 . “Natural Exponential Families With Quadratic Variance Functions,” . The Annals of Statistics , 10 : 65 – 80 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.