×

Jeffreys priors for survival models with censored data. (English) Zbl 0989.62016

Summary: When prior information on model parameters is weak or lacking, Bayesian statistical analyses are typically performed with so-called “default” priors. We consider the problem of constructing default priors for the parameters of survival models in the presence of censoring, using Jeffreys’ rule. We compare these Jeffreys priors to the “uncensored” Jeffreys priors, obtained without considering censored observations, for the parameters of the exponential and log-normal models. The comparison is based on the frequentist coverage of the posterior Bayes intervals obtained from these prior distributions.

MSC:

62F15 Bayesian inference
62N01 Censored data models
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Abel, P. S.; Singpurwalla, N. D., To survive or to fail: that is the question, Am. Statist., 48, 1, 18-21 (1994)
[2] Bartholomew, 1965. A comparison of some Bayes procedures. Biometrika 52, 19-35.; Bartholomew, 1965. A comparison of some Bayes procedures. Biometrika 52, 19-35. · Zbl 0152.17603
[3] Berger, J. O.; Mortera, J., Default Bayes factors for non-nested hypothesis testing, J. Am. Statist. Assoc., 94, 542-554 (1999) · Zbl 0996.62018
[4] Berger, J. O.; Pericchi, L. R., The Intrinsic Bayes factor for model selection and prediction, J. Am. Statist. Assoc., 91, 109-122 (1996) · Zbl 0870.62021
[5] De Santis, F.; Spezzaferri, F., Alternative Bayes factors for model selection, Canadian J. Statist., 25, 503-515 (1997) · Zbl 0894.62031
[6] De Santis, F.; Spezzaferri, F., Methods for robust and default Bayesian model comparison: the fractional Bayes factor approach, Internat. Statist. Rev., 67, 1-20 (1999) · Zbl 0944.62027
[7] Ghosh, J.K., Mukerjee, R., 1992. Non-informative priors. In: Bernardo, J.M.. et al. (Eds.), Bayesian Statistics IV. Oxford University Press, Oxford, pp. 195-210.; Ghosh, J.K., Mukerjee, R., 1992. Non-informative priors. In: Bernardo, J.M.. et al. (Eds.), Bayesian Statistics IV. Oxford University Press, Oxford, pp. 195-210.
[8] Hartigan, J. A., Note on the confidence-prior of Welch and Peers, J. Roy. Statist. Soc. Ser. B, 28, 55-56 (1966) · Zbl 0147.18401
[9] Jeffreys, H., An invariant form for the prior probability in estimation problems, Proc. Roy. Soc. London, Ser. A, 186, 453-461 (1946) · Zbl 0063.03050
[10] Jeffreys, H., Theory of Probability (1961), Oxford University Press: Oxford University Press London · Zbl 0116.34904
[11] Kalbleisch, J. D.; Prentice, R. L., The Statistical Analysis of Failure Time Data. (1980), Wiley: Wiley New York · Zbl 0504.62096
[12] Kass, R. E.; Raftery, A., Bayes factors, J. Am. Statist. Assoc., 90, 773-795 (1995) · Zbl 0846.62028
[13] Kass, R. E.; Wasserman, L., The selection of prior distributions by formal rules, J. Am. Statist. Assoc., 91, 1343-1370 (1995) · Zbl 0884.62007
[14] Lawless, J. F., Statistical Models and Methods for Lifetime Data, Wiley Series in Probab. and Math. Statistics (1982), Wiley: Wiley New York · Zbl 0541.62081
[15] O’Hagan, A., Fractional Bayes factors for model comparison (with discussion), J. Roy. Statist. Soc. Ser. B, 57, 99-138 (1995) · Zbl 0813.62026
[16] Robert, C., The Bayesian Choice. A Decision-Theoretic Motivation. (1994), Springer: Springer Berlin · Zbl 0808.62005
[17] Wasserman, L., 1999. Asymptotic inference for mixture models using data dependent priors. J. Roy. Statist. Soc. Ser. B, to appear.; Wasserman, L., 1999. Asymptotic inference for mixture models using data dependent priors. J. Roy. Statist. Soc. Ser. B, to appear. · Zbl 0976.62028
[18] Welch, B. L.; Peers, H. W., On formulae for confidence points based on integrals of weighted likelihoods, Biometrika, 76, 604-608 (1963) · Zbl 0117.14205
[19] Ye, K., Reference priors when the stopping rule depends on the parameter of interest, J. Am. Statist. Assoc., 88, 360-363 (1993) · Zbl 0773.62061
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.