A generalization of BIC for the general exponential family

Journal of Statistical Planning and Inference

Volumn 136, Issue 9, 2006, Pages 2847-2872

  Chakrabarti, Arijit ^a   Ghosh, Jayanta K ^b,c  

^a OHIO STATE UNIVERSITY   (United States)

^b PURDUE UNIVERSITY   (United States)

^c INDIAN STATISTICAL INSTITUTE   (India)

Author keywords

AIC; Bayes factor; BIC; Laplace approximation; Posterior normality

Indexed keywords

EID: 33646515563     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2005.01.005     Document Type: Article

References (23)

1. Berger J.O., Ghosh J.K., and Mukhopadhyay N. Approximations and consistency of Bayes factors as model dimension grows. J. Statist. Plann. Inference 112 (2003) 241-258
2. Brooks S.P., Catchpole E.P., and Morgan B.J.T. Bayesian animal survival estimation. Statist. Sci. 15 (2000) 357-376
3. Brown, L.D., 1986. In: Gupta, S.S. (Ed.), Fundamentals of Statistical Exponential Families with Applications in Statistical Decision Theory, Institute of Mathematical Statistics Lecture Notes-Monograph Series, vol. 9. Institute of Mathematical Statistics, Hayward, CA.
4. Burnham K.P., and Anderson D.R. Model Selection and Inference-A Practical Information-Theoretic Approach (1998), Springer, Berlin
5. Cox D.R. Analysis of Binary Data (1970), Chapman & Hall, London
6. Ghosh J.K., and Ramamoorti R.V. Bayesian Nonparametrics (2002), Springer, New York
7. Ghosh J.K., and Samanta T.S. Model selection-an overview. Current Sci. 80 (2001) 1135-1144
8. Ghosh J.K., and Samanta T.S. Towards a Non-subjective Bayesian paradigm. In: Misra J.C. (Ed). Uncertainty and Optimality (2002), World Scientific Publishing Company, Singapore
9. Kass R.E., and Raftery A.E. Bayes factors. J. Amer. Statist. Assoc. 90 (1995) 773-795
10. Kass R.E., and Vaidyanathan S. Approximate Bayes factors and orthogonal parameters, with application to testing equality of two binomial proportions. J. Roy. Statist. Soc. Ser. B 54 (1992) 129-144
11. Kass R.E., and Wasserman L. A reference Bayesian test for nested hypotheses and its relationship to the Schwarz criterion. J. Amer. Statist. Assoc. 90 (1995) 928-934
12. Kass, R.E., Tierney, L., Kadane, J.B., 1990. The validity of posterior asymptotic expansions based on Laplace's method. In: S. Geisser, et al. (Eds.), Bayesian and Likelihood Methods in Statistics and Econometrics. North-Holland, New York, pp. 473-488.
13. Pauler D.K. The Schwarz criterion and related methods for normal linear models. Biometrika 85 (1998) 13-27
14. Raftery A.E. Approximate Bayes factors and accounting for model uncertainty in generalized linear models. Biometrika 83 (1996) 251-266
15. Rissanen J. Modelling by shortest data description. Automatica 14 (1978) 465-471
16. Rissanen J. A universal prior for integers and estimation by minimum description length. Ann. Statist. 11 (1983) 416-431
17. Rissanen J. Stochastic complexity. J. Roy. Statist. Soc. Ser. B 49 (1987) 223-239
18. Schwarz G. Estimating the dimension of the model. Ann. Statist. 6 (1978) 461-464
19. Stone M. Comments on model selection criteria of Akaike and Schwarz. J. Roy. Statist. Soc. Ser. B 41 (1979) 276-278
20. Spiegelhalter D.J., Best N.G., Carlin B.P., and van der Linde A. Bayesian measures of model complexity and fit. J. Roy. Statist. Soc. Ser. B 64 (2002) 583-639
21. Volinsky C.T., and Raftery A.E. Bayesian information criterion for censored survival models. Biometrics 56 (2000) 256-262
22. Wilbur J.D., Ghosh J.K., Nakatsu C.H., Brouder S.M., and Doerge R.W. Variable selection in high-dimensional multivariate binary data with application to the analysis of microbial community DNA fingerprints. Biometrics. 58 (2002) 378-386
23. Zellner A., and Siow A. Posterior odds ratios for selected regression hypothesis. In: Bernardo J.M., DeGroot M.H., Lindley D., and Smith A.F.M. (Eds). Bayesian Statistics. Proceedings of the First International Meeting held in Valencia (1980), University of Valencia Press