Nonlocal Priors for High-Dimensional Estimation

Nonlocal priors (NLPs) possess appealing properties for model choice, but their use for estimation has not been studied in detail. We show that for regular models NLP-based Bayesian model averaging (BMA) shrink spurious parameters either at fast polynomial or quasi-exponential rates as the sample size n increases, while nonspurious parameter estimates are not shrunk.

We extend some results to linear models with dimension p growing with n . Coupled with our theoretical investigations, we outline the constructive representation of NLPs as mixtures of truncated distributions that enables simple posterior sampling and extending NLPs beyond previous proposals. Our results show notable high-dimensional estimation for linear models with p > > n at low computational cost.