论文标题
使用KAC定理增强您最喜欢的马尔可夫链蒙特卡洛采样器：kick-kac传送算法
Boost your favorite Markov Chain Monte Carlo sampler using Kac's theorem: the Kick-Kac teleportation algorithm
论文作者
论文摘要
本文重点介绍了在某些一般状态空间上定义的给定目标分布$π$采样的问题。为此，我们介绍了一类新型的非可逆马尔可夫链，每个链条都在扩展状态空间上定义，并且具有不变的概率度量，该概率是承认$π$作为边缘分布的$π$。所提出的方法是受KAC定理的新表述的启发，并允许将全局和局部动态顺利进行。在轻度条件下，相应的马尔可夫过渡内核可以证明是不可还原的，并且会复发。此外，我们确定在全球和局部动力学的适当条件下，几何形状的牙齿性具有。最后，与现有的马尔可夫链蒙特卡洛（MCMC）算法相比，我们以数值说明了所提出的方法的使用及其潜在的好处。
The present paper focuses on the problem of sampling from a given target distribution $π$ defined on some general state space. To this end, we introduce a novel class of non-reversible Markov chains, each chain being defined on an extended state space and having an invariant probability measure admitting $π$ as a marginal distribution. The proposed methodology is inspired by a new formulation of Kac's theorem and allows global and local dynamics to be smoothly combined. Under mild conditions, the corresponding Markov transition kernel can be shown to be irreducible and Harris recurrent. In addition, we establish that geometric ergodicity holds under appropriate conditions on the global and local dynamics. Finally, we illustrate numerically the use of the proposed method and its potential benefits in comparison to existing Markov chain Monte Carlo (MCMC) algorithms.
