Combining a continuous "slab" density with discrete "spike" mass at zero, spike-and-slab priors provide important tools for inducing sparsity and carrying out variable selection in Bayesian models. However, the presence of discrete mass makes posterior inference challenging. "Sticky" extensions to piecewise-deterministic Markov process samplers have shown promising performance, where sampling from the spike is achieved by the process sticking there for an exponentially distributed duration. As it turns out, the sampler remains valid when the exponential sticking time is replaced with its expectation. We justify this by mapping the spike to a continuous density over a latent universe, allowing the sampler to be reinterpreted as traversing this universe while being stuck in the original space. This perspective opens up an array of possibilities to carry out posterior computation under spike-and-slab type priors. Notably, it enables us to construct sticky samplers using other dynamics-based paradigms such as Hamiltonian Monte Carlo; in fact, original sticky process can be established as a partial position-momentum refreshment limit of our Hamiltonian sticky sampler. Our theoretical and empirical findings suggest these alternatives to be at least as efficient as the original sticky approach.

翻译：结合零点的连续“板”密度与离散“尖峰”质量，尖峰-板先验为在贝叶斯模型中诱导稀疏性和执行变量选择提供了重要工具。然而，离散质量的存在使得后验推断具有挑战性。针对分段确定性马尔可夫过程采样器的“粘滞”扩展已展现出有前景的性能，其中通过过程以指数分布持续时间粘滞在尖峰处来实现从尖峰的采样。事实证明，当指数粘滞时间被其期望值替代时，采样器仍然有效。我们通过将尖峰映射到潜在宇宙上的连续密度来证明这一点，从而允许将采样器重新解释为在原始空间中粘滞的同时遍历该宇宙。这一视角为在尖峰-板类型先验下执行后验计算开辟了一系列可能性。值得注意的是，它使我们能够使用其他基于动力学的范式（如哈密顿蒙特卡洛）构建粘滞采样器；实际上，原始粘滞过程可以确立为我们哈密顿粘滞采样器的部分位置-动量更新极限。我们的理论和实证结果表明，这些替代方案至少与原始粘滞方法同样高效。