BAYESIAN ANALYSIS FOR THE WEIBULL PARAMETERS BY USING NONINFORMATIVE PRIOR DISTRIBUTIONS

Fernando A. Moala

Received August 10, 2009

References:

[1] T. R. Bayes, Essay towards solving a problem in the doctrine of chances, 1763. Reprinted in Biometrika 45 (1958), 243-315. [2] J. O. Berger and J. M. Bernardo, On the Development of the Reference Prior Method, Fourth Valencia International Meeting on Bayesian Statistics, Spain, 1992. [3] J. M. Bernardo, Reference posterior distributions for Bayesian inference, J. Roy. Statist. Soc. 41(2) (1979), 113-147. [4] G. E. P. Box and G. C. Tiao, Bayesian Inference in Statistical Analysis, Addison Weiley, 1973. [5] G. C. Canavos and C. P. Tsokos, Bayesian estimation of life parameters in the Weibull distribution, Operations Res. 21 (1973), 755-763. [6] D. R. Cox and N. Reid, Parameter orthogonality and approximate conditional inference, J. Roy. Statist. Soc. Ser. B 49 (1987), 1-39. [7] J. Hartigan, Invariant priors distributions, Ann. Math. Statist. 35 (1964), 836-845. [8] Sir Harold Jeffreys, Theory of Probability, 3rd rev. ed., Oxford Univ. Press, London, 1967. [9] P. S. Laplace, Memoire sur la probabilite des causes par les evenemens, Mem. Acad. R. Sci. Presentes par Divers Savans 6 (1774), 621-656 (English translation: Statist. Sci. 1 (1986), 359-378). [10] D. V. Lindley, On a measure of the information provided by an experiment, Ann. Math. Statist. 27 (1956), 986-1005. [11] D. V. Lindley, The Use of Prior Probability Distributions in Statistical Inference and Decisions, J. Neyman, ed., Proc. Fourth Berkeley Symp. on Math. Statist. Prob., Vol. 1, pp. 453-468, University of California Press, Berkeley, 1961. [12] F. A. Moala, Noinformative priors for Weibull model, 122p. Dissertation (M.Sc degree), ICMSC-USP, Brazil, 1993. [13] D. J. Nordman and W. Q. Meeker, Weibull prediction intervals for a future number of failures, Technometrics 44(1) (2002), 15-23. [14] D. Sun, A note on noninformative priors for Weibull distributions, J. Statist. Planning and Inference 61 (1997), 319-338. [15] R. Tibshirani, Noninformative priors for one parameters of many, Biometrika 76 (1989), 604-608. [16] L. Tierney, R. E. Kass and J. B. Kadane, Fully exponential Laplace approximations to expectations and variances of nonpositive functions, J. Amer. Statist. Assoc. 84(407) (1989), 710-716. [17] A. Zellner, Maximal data information prior distributions, New Methods in the Applications of Bayesian Methods, A. Aykac and C. Brumat, eds., North-Holland, Amsterdam, 1977. [18] A. Zellner, Maximal Data Information Prior Distributions, Basic Issues in Econometrics, Univ. of Chicago Press, 1984. [19] A. Zellner, Bayesian methods and entropy in economics and econometrics, Entropy and Bayesian Methods, W. T. Grandy, Jr. and L. H. Schick eds., Maximum Kluwer Academic Publishers, Dordrecht, Netherlands, 1990, pp. 17-31. [20] A. Zellner and C. K. Min, Bayesian Analysis, Model Selection and Prediction, Technical Report, 1992.

Keywords and phrases: Bayesian, Weibull, posterior, prior, distribution, MDIP, reference prior, information.