Bayesian model averaging and model search strategies

In regression models, such as generalized linear models, there is often substantial prior uncertainty about the choice of covariates to include. Conceptually, the Bayesian paradigm can easily incorporate this form of model uncertainty by building an expanded model that includes all possible subsets of covariates. In Bayesian model averaging, predictive distributions or posterior distributions of quantities of interest are obtained as mixtures of the model-specific distributions weighted by the posterior model probabilities. A major difficulty in implementing this approach is that the number of models in the mixture is often so large that enumeration of all models is impossible and some type of search strategy is required to determine a subset of models to use. In the case of an orthonormal design, some computationally simple approximations to the posterior model probabilities are introduced. These are used to develop efficient methods for deterministic or stochastic sampling from high-dimensional model spaces.