Recent work in BSSVS [51, 52] efficiently performs the exploration in two steps. In the first step, the approach augments the model state-space with a set of P binary indicator variables d~(d 1 , . . . , d P ) and imposes a prior p b ð Þ on the regression coefficients that has expectation 0 and variance proportional to a P|P diagonal matrix with its entries equal to d. If d p~0 , then the prior variance on b p shrinks to 0 and enforces b p~0 in the posterior. In the second step, MCMC explores the joint space of (d, b) simultaneously.