  In many fields, researchers are interested in discovering features with
substantial effect on the response from a large number of features and
controlling the proportion of false discoveries. By incorporating the knockoff
procedure in the Bayesian framework, we develop the Bayesian knockoff filter
(BKF) for selecting features that have important effect on the response. In
contrast to the fixed knockoff variables in the frequentist procedures, we
allow the knockoff variables to be continuously updated in the Markov chain
Monte Carlo. Based on the posterior samples and elaborated greedy selection
procedures, our method can distinguish the truly important features as well as
controlling the Bayesian false discovery rate at a desirable level. Numerical
experiments on both synthetic and real data demonstrate the advantages of our
method over existing knockoff methods and Bayesian variable selection
approaches, i.e., the BKF possesses higher power and yields a lower false
discovery rate.
