Abstract
In Bayesian model selection or testing problems, default priors are typically improper; that is, the resulting Bayes factor is not well defined. To circumvent this problem, two methodologies, namely, intrinsic and fractional Bayes factors are proposed and developed. Further, these two Bayes factors are asymptotically equivalent to the ordinary Bayes factors computed with proper priors called intrinsic priors. However, it seems that there are some necessary conditions to satisfy asymptotic equivalence. Such conditions are derived and justified in this article and illustrative examples are provided. Simulations are performed to demonstrate the results.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Berger, J. O., & Bernardo, J. (1992). On the development of the reference priors. In J. M. Bernardo, J. O. Berger, A. P. Dawid, & A. F. M. Smith (Eds.), Bayesian statistics 4 (pp. 35–60). London: Oxford University Press.
Berger, J. O., & Pericchi, L. (1996). The intrinsic Bayes factor for model selection and prediction. Journal of the American Statistical Association, 91, 109–122.
Geisser, S., & Eddy, W. F. (1979). A predictive approach to model selection. Journal of the American Statistical Association, 74, 153–160.
Kim, S. W. (2000). Intrinsic priors for testing exponential means. Statistics & Probability Letters, 46, 195–201.
Kim, S. W., & Kim, H. (2000). Intrinsic priors for testing two exponentil means with the fractional Bayes factor. Journal of the Korean Statistical Society, 29, 395–405.
Kim, S. W., & Kim, D. H. (2002). Intrinsic priors for two-sample tests in normal populations. Communications in Statistics. Theory and Methods, 31, 1091–1105.
Moreno, E. (1997). Bayes factors for intrinsic and fractional priors in nested models. Bayesian robustness. IMS Lecture Notes-Monograph Series, 31, 257–270.
O’Hagan, A. (1995). Fractional Bayes factors for model comparison. Journal of Royal Statistical Society. Series B, 57, 99–138.
San Martini, A., & Spezzaferri, S. F. (1984). A predictive model selection criterion. Journal of Royal Statistical Society. Series B, 46, 296–303.
Spiegelhalter, D. J., & Smith, A. F. M. (1982). Bayes factors for linear and log-linear models with vague prior information. Journal of Royal Statistical Society. Series B, 44, 377–387.
Sun, D., & Kim, S. W. (1999). Intrinsic priors for testing ordered exponential means. Technical report # 99. National Institute of Statistical Sciences.
Author information
Authors and Affiliations
Corresponding author
Additional information
This research was partially supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 2011-0028933) (Seong W. Kim) and by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (NRF-2014R1A1A2056869) (Jinheum Kim).
Rights and permissions
About this article
Cite this article
Kim, S.W., Kim, J. Asymptotic equivalence between the default Bayes factors and the ordinary Bayes factors with intrinsic priors. J. Korean Stat. Soc. 45, 518–525 (2016). https://doi.org/10.1016/j.jkss.2016.03.002
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1016/j.jkss.2016.03.002