Calibrating bayes factor under prior predictive distributions

Statistica Sinica

Volumn 15, Issue 2, 2005, Pages 359-380

  García Donato, Gonzalo ^a   Chen, Ming Hui ^b  

^a UNIVERSITY OF CASTILLA LA MANCHA   (Spain)

^b UNIVERSITY OF CONNECTICUT   (United States)

Author keywords

Calibrating value; Critical value; Hypothesis testing; Imprecise prior; L measure; Model selection; Monte Carlo; P value; Posterior model probability; Pseudo Bayes factor

Indexed keywords

EID: 20444455108     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Conference Paper

References (27)

1. Aitkin, M. (1991). Posterior Bayes factor (with discussion). J. Roy. Statist. Soc. Ser. B 53, 111-128.
2. Bayarri, M. J. and Berger, J. O. (2000). P values for composite null models (with discussion). J. Amer. Statist. Assoc. 95, 1127-1156.
3. Bayarri, M. J. and Berger, J. O. (1999). Quantifying surprise in the data and model verification. In Bayesian Statistics 6 (Edited by J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith), 53-82. Oxford University Press, Oxford.
4. Berger, J. O. (1985). Statistical Decision Theory and Bayesian Analysis, Second Edition. Springer-Verlag, New York.
5. Berger, J. O., Brown, L. D. and Wolpert, R. L. (1994). A unified conditional frequentist and Bayesian test for fixed and sequential hypothesis testing. Ann. Statist. 22, 1787-1807.
6. Berger, J. O., Boukai, B. and Wang, Y. (1997). Unified frequentist and Bayesian testing of a precise hypothesis (with discussion). Statist. Sci. 12, 133-160.
7. Berger, J. O. and Pericchi, R. L. (2001). Objective Bayesian methods for model selection: introduction and comparison. Model Selection (P. Lahiri Editor), Institute of Mathematical Statistics Lecture Notes- Monograph Series 38.
8. Berger, J. O. and Sellke, T. (1987). Testing a point null hypothesis: the irreconcilability of P values and evidence. J. Amer. Statist. Assoc. 82, 112-122.
9. Box, G. E. P. (1980). Sampling and Bayes' inference in scientific modelling and robustness (with discussion). J. Roy. Statist. Soc. Ser. A 143, 383-430.
10. Carlin, B. P. and Louis, T. A. (2000). Bayes and Empirical Bayes Methods for Data Analysis. Second edition. Chapman and Hall, London.
11. Chen, M.-H. and Shao, Q.-M. (1997). On Monte Carlo methods for estimating ratios of normalizing constants. Ann. Statist. 25, 1563-1594.
12. Chib, S. (1995). Marginal likelihood from the Gibbs output. J. Amer. Statist. Assoc. 90, 1313-1321.
13. Chib, S. and Jeliazkov, I. (2001). Marginal likelihood from the Metropolis-Hastings output. J. Amer. Statist. Assoc. 96, 270-281.
14. DiCiccio, T. J., Kass, R. E., Raftery, A. and Wasserman, L. (1997). Computing Bayes factors by combining simulation and asymptotic approximation. J. Amer. Statist. Assoc. 92, 903-915.
15. Gelfand, A. E. and Ghosh, S. K. (1998). Model choice: a minimum posterior predictive loss approach. Biometrika 85, 1-13.
16. Geisser, S., and Eddy, W. (1979). A predictive approach to model selection. J. Amer. Statist. Assoc. 74, 153-160.
17. Gelman, A. and Meng, X.-L. (1998). Simulating normalizing constants: From importance sampling to bridge sampling to path sampling. Statist. Sci. 13, 163-185.
18. Ibrahim, J. G., Chen, M.-H. and Sinha, D. (2001). Criterion based methods for Bayesian model assessment. Statist. Sinica 11, 419-443.
19. Jeffreys, H. (1961). Theory of Probability. Third edition. Clarendon Press, Oxford.
20. Kass, R. E. and Vaidyanathan, S. (1992). Approximate Bayes factors and orthogonal parameters, with application to testing equality of two binomial proportions. J. Roy. Statist. Soc. Ser. B 54, 129-144.
21. Kass, R. E. and Raftery, A. E. (1995). Bayes factor. J. Amer. Statist. Assoc. 90, 773-795.
22. Lavine, M. and Schervish, M. (1999). Bayes factors: what they are and what they are not. Amer. Statist. 53, 119-122.
23. Meng, X.-L. (1994). Posterior predictive p-values. Ann. Statist. 22, 1142-1160.
24. Meng, X.-L. and Wong, W.H. (1996). Simulating ratios of normalizing constants via a simple identity: a theoretical exploration. Statist. Sinica 6, 831-860.
25. O'Hagan, Q.(1994). Kendall's Advanced Theory of Statistics. Volume 2B: Bayesian Inference. Edward Arnold, London.
26. Vlachos, P. K. and Gelfand, A. E. (2003). On the calibration of Bayesian model choice criteria. J. Statist. Planning and Inference 111, 223-234.
27. Williams, E. (1959). Regression Analysis. Wiley, New York.