  Variable selection has received widespread attention over the last decade as
we routinely encounter high-throughput datasets in complex biological and
environment research. Most Bayesian variable selection methods are restricted
to mixture priors having separate components for characterizing the signal and
the noise. However, such priors encounter computational issues in high
dimensions. This has motivated continuous shrinkage priors, resembling the
two-component priors facilitating computation and interpretability. While such
priors are widely used for estimating high-dimensional sparse vectors,
selecting a subset of variables remains a daunting task. In this article, we
propose a general approach for variable selection with shrinkage priors. The
presence of very few tuning parameters makes our method attractive in
comparison to adhoc thresholding approaches. The applicability of the approach
is not limited to continuous shrinkage priors, but can be used along with any
shrinkage prior. Theoretical properties for near-collinear design matrices are
investigated and the method is shown to have good performance in a wide range
of synthetic data examples.
