  In many scientific fields, researchers are interested in discovering features
with substantial effect on the response from a large number of features while
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 a frequentist procedure, we allow
the knockoff variables to be continuously updated using the Markov chain Monte
Carlo. Based on the posterior samples and the elaborated greedy selection
procedure, our method can distinguish the truly important features from
unimportant ones and the Bayesian false discovery rate can be controlled at a
desirable level. Numerical experiments on both synthetic and real data
demonstrate the advantages of our BKF over existing knockoff methods and
Bayesian variable selection approaches, i.e., the BKF possesses higher power
and yields a lower false discovery rate.
