Bernstein-von Mises theorem for sparse generalized linear models
稀疏广义线性模型的 Bernstein–von Mises 定理
We establish an oracle Bernstein-von Mises theorem for high-dimensional sparse generalized linear models under an outcome-independent spike-and-slab prior. The posterior consistently recovers the true active set and converges in total variation to the Gaussian law that would arise if this set were known in advance, even when the active dimension grows. The result holds for both ordinary and fractional posteriors, the latter with the expected variance inflation under…