## ABSTRACT

In this chapter, we describe a new procedure, introduced in George and McCulloch (1993), which stochastically searches for 'promising' subsets of predictors. This procedure, which we call stochastic search variable selection (SSVS), puts a probability distribution on the set of all possible regression models such that 'promising' models are given highest probability, and then uses the Gibbs sampler to simulate a correlated sample from this distribution. The more promising models are then easily identified as those which appear with highest frequency in this sample. This approach can be effective even when the size of the simulated sample is much smaller than the number of possible models (2P), since the vast majority of the models will have very small probability and can be ignored. We have successfully applied SSVS to problems with hundreds of potential predictors (see George and McCulloch, 1994).