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Rejoinder: Bayesian checking of the second levels of hierarchical models. (English) Zbl 1246.62030

Rejoinder to the comments of M. Evans [ibid. 22, No. 3, 344–348 (2007; Zbl 1246.62036)], A. Gelman [ibid. 22, No. 3, 349–352 (2007; Zbl 1246.62042)], V.E. Johnson, [ibid. 22, No. 3, 353–358 (2007; Zbl 1246.62048)], M.D. Larsen and L. Lu [ibid. 22, No. 3, 359–362 (2007; Zbl 1246.62053)] on the authors’ article, ibid. 22, No. 3, 322–343 (2007; Zbl 1246.62029).

MSC:

62F15 Bayesian inference
62C12 Empirical decision procedures; empirical Bayes procedures

References:

[1] Bayarri, M. J. and Berger, J. O. (1997). Measures of surprise in Bayesian analysis. ISDS Discussion Paper 97–46, Duke Univ.
[2] Bayarri, M. J. and Berger, J. O. (1999). Quantifying surprise in the data and model verification. In Bayesian Statistics 6 (J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.) 53–82. Oxford Univ. Press. · Zbl 0974.62021
[3] Bayarri, M. J. and Berger, J. O. (2000). \(p\)-values for composite null models (with discussion). J. Amer. Statist. Assoc. 95 1127–1142, 1157–1170. JSTOR: · Zbl 1004.62022 · doi:10.2307/2669749
[4] Bayarri, M. J., Castellanos, M. E. and Morales, J. (2006). MCMC methods to approximate conditional predictive distributions. Comput. Statist. Data Anal. 51 621–640. · Zbl 1157.62355 · doi:10.1016/j.csda.2006.01.018
[5] Fraser, D. A. S. and Rousseau, J. (2005). Developing \(p\)-values: A Bayesian-frequentist convergence. Cahier du CEREMADE, Univ. Paris Dauphine, France.
[6] Hubbard, R. and Bayarri, M. J. (2003). Confusion over measures of evidence (p’s) versus errors (\(\alpha\)’s) in classical statistical testing (with discussion). Amer. Statist. 57 171–182. · doi:10.1198/0003130031856
[7] Robert, C. P. and Rousseau, J. (2002). A mixture approach to Bayesian goodness of fit. Cahier du CEREMADE, 02009, Univ. Paris Dauphine, France.
[8] Robins, J. M. (1999). Discussion of quantifying surprise in the data and model verification. In Bayesian Statistics 6 (J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.) 67–70. Oxford Univ. Press. · Zbl 0974.62021
[9] Robins, J. M., van der Vaart, A. and Ventura, V. (2000). Asymptotic distribution of \(p\) values in composite null models (with discussion). J. Amer. Statist. Assoc. 95 1143–1156, 1171–1172. JSTOR: · Zbl 1072.62522 · doi:10.2307/2669750
[10] Sellke, T., Bayarri, M. J. and Berger, J. O. (2001). Calibration of \(p\)-values for testing precise null hypotheses. Amer. Statist. 55 62–71. JSTOR: · Zbl 1182.62053 · doi:10.1198/000313001300339950
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