Publication Cover
Statistics
A Journal of Theoretical and Applied Statistics
Volume 49, 2015 - Issue 5
109
Views
7
CrossRef citations to date
0
Altmetric
Original Articles

Prior near ignorance for inferences in the k-parameter exponential family

&
Pages 1104-1140 | Received 09 Apr 2013, Accepted 11 Aug 2014, Published online: 02 Oct 2014

References

  • Jeffreys H. Theory of probability. 3rd ed. Oxford: Clarendon Press; 1983.
  • Berger JO. Statistical decision theory and Bayesian analysis. New York: Springer Series in Statistics; 1985.
  • Bernardo JM, Smith AFM. Bayesian theory. Chichester, UK: John Wiley & Sons; 1994.
  • Stone M. Review and analysis of some inconsistencies related to improper priors and finite additivity. Stud Logic Found Math. 1982;104:413–426. doi: 10.1016/S0049-237X(09)70210-1
  • Hill BM, Lane D. Conglomerability and countable additivity. Sankhyā. 1985;366–379.
  • Walley P. Statistical reasoning with imprecise probabilities. New York: Chapman and Hall; 1991.
  • Berger JO, Moreno E, Pericchi LR, Bayarri MJ, Bernardo A, Cano JA, De la Horra J, Martín J, Ríos-Insúa D, Betrò B, Dasgupta A, Gustafson P, Wasserman L, Kadane JB, Srinivasan C, Lavine M, O'Hagan A, Polasek W, Robert CP, Goutis C, Ruggeri F, Salinetti G, Sivaganesan S. An overview of robust Bayesian analysis. Test. 1994;3(1):5–124. doi: 10.1007/BF02562676
  • Huber PJ. The use of Choquet capacities in statistics. Bull Int Statist Inst. 1973;45(4):181–191.
  • Sivaganesan S, Berger JO. Ranges of posterior measures for priors with unimodal contaminations. Ann Statist. 1989;17(2):868–889. doi: 10.1214/aos/1176347148
  • DeRoberts L, Hartigan JA. Bayesian inference using intervals of measures. Ann Statist. 1981;9(2):235–244. doi: 10.1214/aos/1176345391
  • Pericchi LR, Walley P. Robust Bayesian credible intervals and prior ignorance. Int Statist Rev. 1991;58:1–23. doi: 10.2307/1403571
  • Huber PJ. Robust estimation of a location parameter. Ann Math Statist. 1964;35(1):73–101. doi: 10.1214/aoms/1177703732
  • Benavoli A, Zaffalon M. A model of prior ignorance for inferences in the one-parameter exponential family. J Statist Plann Inference. 2012;142(7):1960–1979. doi: 10.1016/j.jspi.2012.01.023
  • Walley P. A bounded derivative model for prior ignorance about a real-valued parameter. Scand J Statist. 1997;24(4):463–483. doi: 10.1111/1467-9469.00075
  • Coolen FPA, Augustin T. A nonparametric predictive alternative to the imprecise Dirichlet model: the case of a known number of categories. Internat J Approx Reason. 2009;50(2):217–230. doi: 10.1016/j.ijar.2008.03.011
  • DasGupta A. Asymptotic theory of statistics and probability. New York: Springer; 2008.
  • Brown LD. Fundamentals of statistical exponential families: with applications in statistical decision theory. Hayward, CA: IMS; 1986.
  • Barndorff-Nielsen O. Information and exponential families in statistical inference. New York: Wiley; 1978.
  • Letac G. Lectures on natural exponential families and their variance functions, Number 50. Conselho Nacional de Desenvolvimento Científico e Tecnológico, Instituto de Matemática Pura e Aplicada; 1992.
  • Diaconis P, Ylvisaker D. Conjugate priors for exponential families. Ann Statist. 1979;7(2):269–281. doi: 10.1214/aos/1176344611
  • Walley P. Inferences from multinomial data: learning about a bag of marbles. J R Stat Soc Ser B Methodol. 1996;58(1):3–57.
  • Bernard J-M. An introduction to the imprecise Dirichlet model for multinomial data. Internat J Approx Reason. 2005;39(2–3):123–150. doi: 10.1016/j.ijar.2004.10.002
  • Gelman A, Carlin JB, Stern HS, Rubin DB. Bayesian data analysis. Boca Raton: CRC Press; 2004.
  • Hartigan J. Invariant prior distributions. Ann Math Statist. 1964;836–845. doi: 10.1214/aoms/1177703583
  • Kass RE, Wasserman L. The selection of prior distributions by formal rules. J Amer Statist Assoc. 1996;1343–1370. doi: 10.1080/01621459.1996.10477003
  • Regazzini E. De finetti's coherence and statistical inference. Ann Statist. 1987;845–864. doi: 10.1214/aos/1176350379

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.