Abstract
Previous approaches to establishing posterior consistency of Bayesian regression problems have used general theorems that involve verifying sufficient conditions for posterior consistency. In this article, we consider a direct approach by computing the posterior density explicitly and evaluating its asymptotic behavior. For this purpose, we deal with a sample size dependent prior based on a truncated regression function with increasing sample size, and evaluate the asymptotic properties of the resulting posterior. Based on a concept called posterior density consistency, we attempt to understand posterior consistency. As an application, we illustrate that the posterior density of an orthogonal semiparametric regression model is consistent.
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Acknowledgments
The authors are very grateful to the two referees for constructive comments. Research of Seongbaek Yi was supported by the Pukyong National University Research Foundation in 2006(PS-2006-011). Research of Taeryon Choi was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2009-0063906).