VARIABLE SELECTION VIA GIBBS SAMPLING

A crucial problem in building a multiple regression model is the selec tion of predictors to include. The main thrust of this article is to p ropose and develop a procedure that uses probabilistic considerations for selecting promising subsets. This procedure entails embedding the regression setup in a hierarchical normal mixture model where latent v ariables are used to identify subset choices. In this framework the pr omising subsets of predictors can be identified as those with higher p osterior probability. The computational burden is then alleviated by u sing the Gibbs sampler to indirectly sample from this multinomial post erior distribution on the set of possible subset choices. Those subset s with higher probability-the promising ones-can then be identified by their more frequent appearance in the Gibbs sample.