An intriguing new class of piecewise deterministic Markov processes (PDMPs) has recently been proposed as an alternative to Markov chain Monte Carlo (MCMC). In order to facilitate the application to a larger class of problems, we propose a new class of PDMPs termed Gibbs zig-zag samplers, which allow parameters to be updated in blocks with a zig-zag sampler applied to certain parameters and traditional MCMC-style updates to others. We demonstrate the flexibility of this framework on posterior sampling for logistic models with shrinkage priors for high-dimensional regression and random effects and provide conditions for geometric ergodicity and the validity of a central limit theorem.
翻译:最近,作为Markov连锁公司Monte Carlo(MCMC)的替代方案,提出了一种令人感兴趣的新种类的碎片确定式Markov工艺(PDMPs),作为Markov 链Monte Carlo(MCMC)的替代方案。 为了便利对更大种类的问题的应用,我们提议了一种新的PDMPs类别,称为Gibbs zig-zag采样器,允许在区块内更新参数,将zig-zag采样器用于某些参数和传统的MCMC式更新到其他参数。我们展示了这一框架在后方取样的后勤模型方面的灵活性,这些模型具有高维回归和随机效应的缩缩缩前功能,并为几何理论性和中心界限理论的有效性提供了条件。