Title: High-dimensional posterior consistency for hierarchical non-local priors in regression,
Abstract: 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 $p$ is bounded by the number of observations $n$ and establish strong
model selection consistency when $p$ is allowed to increase at a polynomial
rate with $n$. Through simulation studies, we demonstrate that our model
selection procedure outperforms commonly used penalized likelihood methods in a
range of simulation settings.