|
Abstract:
|
Zellner’s g-priors are popular in Bayesian regression modeling. There are many studies in Bayesian model selection consistency for the g-priors. However, there is limited research on model selection consistency in Bayesian high-dimensional regression with the g-priors. In this study, we explore the consistency of the posterior model distribution induced by the g-prior in a high-dimensional regression framework, in which the number of potential predictors can grow as the sample size increases. We further allow the number of the potential predictors to grow at a higher rate along with the sample size which is an increasingly common assumption in high-dimensional data analysis. In the high-dimensional setting, we establish sufficient conditions to achieve the model selection consistency with the g-priors. In addition, we examine finite sample behavior of the posterior model distribution via a simulation study. Our result shows that, when the g-prior satisfies our conditions, the model posterior tends to be the point mass distribution at the true model as the sample size grows. On the contrary, any violation of our conditions leads to inconsistency.
|
