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Extended Bayesian information criteria for model selection with large model spaces
Department of Statistics, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada jhchen{at}stat.ubc.ca
Department of Statistics and Applied Probability, National University of Singapore, Singapore 117546 stachenz{at}nus.edu.sg
Received for publication 1 January 2007. Revision received 1 January 2008.
The ordinary Bayesian information criterion is too liberal for model selection when the model space is large. In this paper, we re-examine the Bayesian paradigm for model selection and propose an extended family of Bayesian information criteria, which take into account both the number of unknown parameters and the complexity of the model space. Their consistency is established, in particular allowing the number of covariates to increase to infinity with the sample size. Their performance in various situations is evaluated by simulation studies. It is demonstrated that the extended Bayesian information criteria incur a small loss in the positive selection rate but tightly control the false discovery rate, a desirable property in many applications. The extended Bayesian information criteria are extremely useful for variable selection in problems with a moderate sample size but with a huge number of covariates, especially in genome-wide association studies, which are now an active area in genetics research.
Key Words: Bayesian paradigm • Consistency • Genome-wide association study • Tournament approach • Variable selection
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