Post-processing posterior predictive p values

Journal of the American Statistical Association

Volumn 101, Issue 475, 2006, Pages 1157-1174

  Hjort, Nils Lid ^a   Dahl, Fredrik A ^b   Steinbakk, Gunnhildur Högnadóttir ^a  

^a UNIVERSITY OF OSLO   (Norway)

^b AKERSHUS UNIVERSITY HOSPITAL   (Norway)

Author keywords

Calibration of ppp values; Dipper data; Double simulation; Model criticism; Posterior predictive p values; Prior construction; Prior predictive evaluation; Surprise

Indexed keywords

EID: 33748861054     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/016214505000001393     Document Type: Review

References (37)

1. Bayarri, M. J., and Berger, J. O. (2000), "P Values in Composite Null Models" (with discussion), Journal of the American Statistical Association, 95, 1127-1142.
2. _ (2004), "The Interplay of Bayesian and Frequentist Analysis," Statistical Science, 19, 58-80.
3. Bayarri, M. J., and Castellanos, M. E. (2004), "Bayesian Checking of Hierarchical Models," technical report. University of Valencia.
4. Billingsley, P. (1968), Convergence of Probability Measures, Singapore: Wiley.
5. Box, G. E. P. (1980), "Sampling and Bayes' Inference in Scientific Modelling and Robustness," Journal of the Royal Statistical Society, Ser. A, 143, 383-430.
6. Brooks, S. P., Catchpole, E. A., and Morgan, B. J. T. (2000), "Bayesian Animal Survival Estimation," Statistical Science, 15, 357-376.
7. Claeskens, G., and Hjort, N. L. (2003), "The Focused Information Criterion" (with discussion). Journal of the American Statistical Association, 98, 900-916 and 938-945.
8. Clyde, M., and George, E. (2004), "Model Uncertainty," Statistical Science, 19, 81-94.
9. Dey, D. K., Gelfand, A. E., Swartz, T. B., and Vlachos, P. K. (1998), "A Simulation-Intensive Approach for Checking Hierarchical Models," Test. 7, 325-346.
10. Gelfand, A. E., and Dey, D. K. (1994), "Bayesian Model Choice: Asymplotics and Exact Calculations," Journal of the Royal Statistical Society, Ser. B, 56, 501-514.
11. Gelfand, A. E., and Ghosh, S. K. (1998), "Model Choice: A Minimum Posterior Predictive Approach," Biometrika, 85, 1-11.
12. Gelfand, A. E., and Wang, F. (2002). "A Simulation Based Approach to Sample Size Determination Under a Given Model and for Separating Models," Statistical Science, 17, 193-208.
13. Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B. (2004), Bayesian Data Analysis (2nd ed.), Boca Raton, FL: Chapman & Hall/CRC.
14. Gelman, A., Meng, X.-L., and Stem, H. (1996), "Posterior Predictive Assessment of Model Fitness via Realized Discrepancies" (with discussion), Statistica Sinica, 6, 733-807.
15. Good, I. J. (1983). Good Thinking: The Foundations of Probability and Its Applications, Minneapolis: University of Minnesota Press.
16. Guttiérrez-Peña, E., and Walker, S. G. (2001), "A Bayesian Predictive Approach to Model Selection," Journal of Statistical Planning and Inference, 93, 259-276.
17. Guttman, I. (1967). "The Use of the Concept of a Future Observation in Goodness-of-Fit Problems," Journal of the Royal Statistical Society, Ser. B, 29, 83-100.
18. Hjort, N. L. (2003a), "Catriona LeMay Doan: Going for Gold" [book review], SpeedSkating World, 8, 14-15.
19. _ (2003b), "Topics in Nonparametric Bayesian Statistics" (with discussion), in Highly Structured Stochastic Systems, eds. P. J. Green, N. L. Hjort, and S. Richardson, Oxford, U.K.: Oxford University Press, pp. 455-478.
20. _ (2005), "The Bolshoi of Speedskating," SpeedSkating World, 10, 14-17.
21. Hjort, N. L., and Claeskens, G. (2003), "Frequentist Model Average Estimators" (with discussion). Journal of the American Statistical Association, 98, 879-899 and 938-945.
22. Hjort, N. L., and Ongaro, A. (2005), "Exact Inference for Random Dirichlet Means," Statistical Inference for Stochastic Processes, 8, 227-254.
23. Kadane, J. B., and Lazar, N. A. (2004), "Methods and Criteria for Model Selection," Journal of the American Statistical Association, 99, 279-290.
24. Kass, R. E., and Raftery, A. E. (1995), "Bayes Factors," Journal of the American Statistical Association, 90, 773-795.
25. Lebreton, J.-D., Burnham, K. P., Clobert, J., and Anderson, D. R. (1992), "Modeling Survival and Testing Biological Hypotheses Using Marked Animals: A Unified Approach With Case Studies," Ecological Monographs, 62, 67-118.
26. Lehmann, E. L. (1983), Theory of Point Estimation, New York: Wiley.
27. Lu, H., Hodges, J. S., and Carlin, B. P. (2006), "Measuring the Complexity of Generalized Linear Hierarchical Models," Biostatistics, to appear.
28. Marden, J. I. (2000), "Hypothesis Testing: From p Values to Bayes Factors," Journal of the American Statistical Association, 95, 1316-1320.
29. Meng, X.-L. (1994), "Posterior Predictive p Values," The Annals of Statistics, 22, 1142-1160.
30. O'Hagan, T. (2003), "HSSS Model Criticism" (with discussion), in Highly Structured Stochastic Systems, eds. P. J. Green, N. L. Hjort, and S. Richardson, Oxford, U.K.: Oxford University Press, pp. 423-453.
31. Robert, C. P. (2001), The Bayesian Choice (2nd ed.), New York: Springer-Verlag.
32. Robins, J. M., van der Vaart, A., and Ventura, V. (2000), "Asymptotic Distribution of p Values in Composite Null Models" (with discussion), Journal of the American Statistical Association, 95, 1143-1156.
33. Rubin, D. B. (1984), "Bayesianly Justifiable and Relevant Frequency Calculations for the Applied Statistician," The Annals of Statistics, 12, 1151-1172.
34. Sinharay, S., and Stern, H. S. (2003), "Posterior Predictive Model Checking in Hierarchical Models," Journal of Statistical Planning and Inference, 111, 209-221.
35. Smith, A. F. M., and Spiegelhalter, D. J. (1980), "Bayes Factors and Choice Criteria for Linear Models," Journal of the Royal Statistical Society, Ser. B, 42, 213-220.
36. Spiegelhalter, D. J., Best, N. G., Carlin, B. P., and van der Linde, A. (2002), "Bayesian Measures of Model Complexity and Fit" (with discussion). Journal of the Royal Statistical Society, Ser. B, 64, 583-639.
37. van der Linde, A. (2004), "On the Association Between a Random Variable and an Observable," Test, 13, 85-111.