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Spike-and-slab priors are popular Bayesian solutions for high-dimensionallinear regression problems. Previous theoretical studies on spike-and-slabmethods focus on specific prior formulations and use prior-dependent conditionsand analyses, and thus can not be generalized directly. In this paper, wepropose a class of generic spike-and-slab priors and develop a unifiedframework to rigorously assess their theoretical properties. Technically, weprovide general conditions under which generic spike-and-slab priors canachieve the nearly-optimal posterior contraction rate and the model selectionconsistency. Our results include those of Narisetty and He (2014) and Castilloet al. (2015) as special cases.

Bayesian high-dimensional linear regression with generic spike-and-slab priors