We derive a novel non-reversible, continuous-time Markov chain Monte Carlo sampler, called Coordinate Sampler, based on a piecewise deterministic Markov process, which is a variant of the Zigzag sampler of Bierkens et al. (Ann Stat 47(3):1288–1320, 2019). In addition to providing a theoretical validation for this new simulation algorithm, we show that the Markov chain it induces exhibits geometrical ergodicity convergence, for distributions whose tails decay at least as fast as an exponential distribution and at most as fast as a Gaussian distribution. Several numerical examples highlight that our coordinate sampler is more efficient than the Zigzag sampler, in terms of effective sample size.

中文翻译：

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坐标采样器：不可逆的吉布斯样MCMC采样器

我们基于分段确定性马尔可夫过程推导了一种新颖的不可逆的，连续时间的马尔可夫链蒙特卡洛采样器，称为坐标采样器，它是Bierkens等人的之字形采样器的一种变体。（Ann Stat 47（3）：1288-1320，2019）。除了为这种新的仿真算法提供理论验证之外，我们还表明，对于尾部衰减至少与指数分布一样快且至多与高斯分布一样快的分布，它引起的马尔可夫链表现出了几何遍历收敛性。几个数值示例表明，就有效样本量而言，我们的坐标采样器比之字形采样器更有效。