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Abstract:
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In the variable selection framework, implementation of Bayesian model averaging often becomes non-trivial, due to the vastness of the model space, or intractable marginal likelihoods, or both. However for orthogonal design matrices with appropriate prior structures, posterior probabilities of models can be calculated without enumerating the entire model space. We propose a novel method called Orthogonal Data Augmentation (ODA), which augments the design matrix with rows to obtain a new design matrix whose columns are orthogonal. We show how to construct such a design and develop MCMC algorithms for posterior computation. In particular ODA allows us to construct estimates of the mass of unsampled models and provide valuable information regarding how much of the model space has been explored.
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