  The MC$^3$ (Madigan and York, 1995) and Gibbs (George and McCulloch, 1997)
samplers are the most widely implemented algorithms for Bayesian Model
Averaging (BMA) in linear regression models. These samplers draw a variable at
random in each iteration using uniform selection probabilities and then propose
to update that variable. This may be computationally inefficient if the number
of variables is large and many variables are redundant. In this work, we
introduce adaptive versions of these samplers that retain their simplicity in
implementation and reduce the selection probabilities of the many redundant
variables. The improvements in efficiency for the adaptive samplers are
illustrated in real and simulated datasets.
