We consider Bayesian linear regression with sparsity-inducing prior and design efficient sampling algorithms leveraging posterior contraction properties. A quasi-likelihood with Gaussian spike-and-slab (that is favorable both statistically and computationally) is investigated and two algorithms based on Gibbs sampling and Stochastic Localization are analyzed, both under the same (quite natural) statistical assumptions that also enable valid inference on the sparse planted signal. The benefit of the Stochastic Localization sampler is particularly prominent for data matrix that is not well-designed.

翻译：我们考虑具有稀疏诱导先验的贝叶斯线性回归，并利用后验收缩性质设计高效采样算法。研究了一种基于高斯Spike-and-Slab的准似然方法（该算法在统计与计算上均具有优势），并在相同的（相当自然的）统计假设下分析了基于Gibbs采样和随机局部化（Stochastic Localization）的两种算法。这些假设同样能够对稀疏植入信号进行有效推断。当数据矩阵设计不佳时，随机局部化采样器的优势尤为显著。