For large model spaces, the potential entrapment of Markov chain Monte Carlo (MCMC) based methods with spike-and-slab priors poses significant challenges in posterior computation in regression models. On the other hand, maximum a posteriori (MAP) estimation, which is a more computationally viable alternative, fails to provide uncertainty quantification. To address these problems simultaneously and efficiently, this paper proposes a hybrid method that blends MAP estimation with MCMC-based stochastic search algorithms within a heavy-tailed error framework. Under hyperbolic errors, the current work develops a two-step expectation conditional maximization (ECM) guided MCMC algorithm. In the first step, we conduct an ECM-based posterior maximization and perform variable selection, thereby identifying a reduced model space in a high posterior probability region. In the second step, we execute a Gibbs sampler on the reduced model space for posterior computation. Such a method is expected to improve the efficiency of posterior computation and enhance its inferential richness. Through simulation studies and benchmark real life examples, our proposed method is shown to exhibit several advantages in variable selection and uncertainty quantification over various state-of-the-art methods.

翻译：对于大型模型空间，基于尖峰-平板先验的马尔可夫链蒙特卡洛（MCMC）方法可能陷入局部区域，这给回归模型中的后验计算带来了重大挑战。另一方面，最大后验概率（MAP）估计作为一种计算上更可行的替代方案，却无法提供不确定性量化。为同时高效解决这些问题，本文提出了一种混合方法，在厚尾误差框架下将MAP估计与基于MCMC的随机搜索算法相结合。在双曲误差假设下，本研究开发了一种两步式的期望条件最大化（ECM）引导MCMC算法。第一步，我们执行基于ECM的后验最大化并进行变量选择，从而在高后验概率区域确定一个降维的模型空间。第二步，我们在降维后的模型空间上运行吉布斯采样器进行后验计算。该方法有望提升后验计算的效率并增强其推断丰富性。通过模拟研究和基准现实案例验证，我们提出的方法在变量选择和不确定性量化方面相较于多种先进方法展现出多项优势。