High-dimensional posterior consistency for hierarchical non-local priors in regression
The choice of tuning parameter in Bayesian variable selection is a critical problem in modern statistics. Especially in the related work of nonlocal prior in regression setting, the scale parameter reflects the dispersion of the non-local prior density around zero, and implicitly determines the size of the regression coefficients that will be shrunk to zero. In this paper, we introduce a fully Bayesian approach with the pMOM nonlocal prior where we place an appropriate Inverse-Gamma prior on the tuning parameter to analyze a more robust model that is comparatively immune to misspecification of scale parameter. Under standard regularity assumptions, we extend the previous work where is bounded by the number of observations and establish strong model selection consistency when is allowed to increase at a polynomial rate with . Through simulation studies, we demonstrate that our model selection procedure outperforms commonly used penalized likelihood methods in a range of simulation settings.