Abstract
In this paper we present methods to verify whether a prior distribution coincides with a sample or not within Bayes statistics. We present methods to generalize well known classical tests to this problem and construct a new test. An additional method is based on comparison between prior and posterior distribution. We illustrate the theory with applications to the Exponential distribution.
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Bibliography
Abdel-Wahid A A, A Winterbottom (1987) Approximate Bayesian Estimators for the Weibull Reliability Function and Hazard Rate from Censored Data. J Statist Plann Inf 14: 277–283.
Ashour S K, E Shonkry, T Mohamed (1983) Bayesian Estimation for Compound Weibull Model. Math Oper Res, ser Statistics 14: 381–380.
Billingsley P (1968) Convergence of Probability Measures. J Wiley & Sons, New York/London/Sydney/Toronto.
Bozdogan H (1987) Model Selection and Akaike's Information Criterion (AIC): The General Theory and its Analytical Extensions. Psychometrika 52: 345–370.
Cox D R, D V Hinkley (1974). Theoretical Statistics, Chapmann & Hall, London.
Ellis W C, V M Kao Tammala (1986) Minimum Expected Loss Estimators of the Shape and Scale Parameters of the Weibull Distributions. IEEE Trans Reliability R-35: 212–215.
Fernholz L T (1983) Von Mises Calculus for Statistical Functionals. Lecture Notes Statist. 19, Springer-Verlag, New York/Heidelberg/Tokyo.
Hjorth U (1989) On Model Selection in the Computer Age. J. Statist. Plann. Inf. 23: 101–115.
Ibragimov I A, R S Hasminski (1979). Asymptotic Estimation Theory (in Russian), Nauka, Moskwa.
Koziol J A, S B Green (1976) A Cramér-von-Mises Statistic for Randomly Censored Data. Biometrika 63: 465–474.
Pandey M (1987) Bayes Estimator of Survival Probability from Randomly Censored Observations with Weibull Distributions of Time to Death. 29: 491–496.
Raiffa H, R Schlaiffer (1977) Applied Statistical Decision Theory, M.I.T. Press.
Schmetterer L (1966) Einführung in die mathematische Statistik. Springer-Verlag, Wien/New York.
Singpurwalla N D (1988) An Interactive PC-Based Procedure for Reliability Assessment Incorporating Expert Opinion and Survival Data. J Amer Statist Assoc. 83: 43–51.
Singpurwalla N D, M S Song (1988) Reliability Analysis Using Weibull Life Time Data and Expert Opinion. IEEE Trans Reliability R-37: 340–347.
Sinha S K (1987) Bayesian Estimation of the Parameters and Reliability Function of a Mixture of Weibull Life Distributions. J Statist Plann Inf 14: 377–387.
Sinha S K, J A Sloan (1988) Bayes Estimation of the Parameters and Reliability Functions of the 3-parameter Weibull-Distribution. IEEE Trans. Reliability R-37: 364–369.
Stephens M A (1974) EDF-Statistics for Goodness-of-Fit and Some Comparisons. J Amer Statist Assoc. 69: 730–737.
Tziafetas G N (1987) On the Construction of Bayesian Prediction Limits for the Weibull Distribution. Statistics 18: 623–628.
Wang Qun (1991) A Modification of Bayesian Approach in Nuclear Plant Data Analysis. Microelectronics & Reliab. 31: 1137–1142.
Zellner A (1971) An Introduction to Bayesian Inference in Econometrics. J. Wiley & Sons, New York/London/Sydney/Toronto.
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Schäbe, H. Post-data evaluation of prior assessment. Statistical Papers 34, 339–361 (1993). https://doi.org/10.1007/BF02925553
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DOI: https://doi.org/10.1007/BF02925553