Implementing Bayesian variable selection for linear Gaussian regression models for analysing high dimensional data sets is of current interest in many fields. In order to make such analysis operational, we propose a new sampling algorithm based upon Evolutionary Monte Carlo and designed to work under the "large p, small n" paradigm, thus making fully Bayesian multivariate analysis feasible, for example, in genetics/genomics experiments. Two real data examples in genomics are presented, demonstrating the performance of the algorithm in a space of up to 10,000 covariates. Finally the methodology is compared with a recently proposed search algorithms in an extensive simulation study.
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