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Abstract:
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When analyzing data from a screening design, we are most interested in performing model selection that respects the three effect principles: sparsity, hierarchy, and heredity. The Stochastic Search Variable Selection (SSVS) algorithm uses Gibbs sampling to perform model selection based on a special set of prior distributions. Each potential effect has a prior that is a mixture distribution of two mean-zero normals with different variances, depending on whether an effect is thought to be active or not. Active effects have a diffuse prior, which leads to a posterior driven mainly by the data. While the conjugacy of these priors allow the Gibbs sampler to efficiently sample from the conditional posterior distributions, assigning a zero-mean prior to an active effect seems inappropriate and non-intuitive. In this talk, we introduce two new sets of prior distributions that better respect the effect principles and allow for additional prior information about effect directions. Through a simulation study, we demonstrate their superior performance to the conventional SSVS approach.
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