Bayesian variable selection in generalized linear models using a combination of stochastic optimization methods

In this paper the usage of a stochastic optimization algorithm as a model search tool is proposed for the Bayesian variable selection problem in generalized linear models. Combining aspects of three well known stochastic optimization algorithms, namely, simulated annealing, genetic algorithm and tabu search, a powerful model search algorithm is produced. After choosing suitable priors, the posterior model probability is used as a criterion function for the algorithm; in cases when it is not analytically tractable Laplace approximation is used. The proposed algorithm is illustrated on normal linear and logistic regression models, for simulated and real‐life examples, and it is shown that, with a very low computational cost, it achieves improved performance when compared with popular MCMC algorithms, such as the MCMC model composition, as well as with ‘vanilla’ versions of simulated annealing, genetic algorithm and tabu search.