论文标题
关于大都市杂货算法的接受机制
On the accept-reject mechanism for Metropolis-Hastings algorithms
论文作者
论文摘要
这项工作开发了一个强大而多才多艺的框架，用于确定大都市杂物类型的马尔可夫内核中广泛用于统计抽样问题的接受比。我们的方法使我们能够得出新的内核类别，这些内核统一随机步行或扩散型采样方法，其基于汉密尔顿动力学的思想的更为复杂的“扩展相位空间”算法。我们的起点是在可测量状态空间的一般性中产生的抽象结果，该空间解决了具有一定的参与结构的建议内核。请注意，尽管这种基本提案结构提出了一个包括汉密尔顿型内核在内的范围，但我们证明，我们的抽象结果在适当的意义上是相当于[Tierney，Applied-ofied-ofiedine of Applied-opiedine of Applied-operiedine of Applied-operiedine of Applied-operiedine of Applied-operiedine of Applied-opparied-ofiendiention，1998]的范围，其中与汉密尔顿方法的联系更加晦涩难懂。总的来说，我们主要结果的理论统一和覆盖范围为推导新型采样算法提供了基础，同时在现有方法之间建立了裸露的重要关系。
This work develops a powerful and versatile framework for determining acceptance ratios in Metropolis-Hastings type Markov kernels widely used in statistical sampling problems. Our approach allows us to derive new classes of kernels which unify random walk or diffusion-type sampling methods with more complicated "extended phase space" algorithms based around ideas from Hamiltonian dynamics. Our starting point is an abstract result developed in the generality of measurable state spaces that addresses proposal kernels that possess a certain involution structure. Note that, while this underlying proposal structure suggests a scope which includes Hamiltonian-type kernels, we demonstrate that our abstract result is, in an appropriate sense, equivalent to an earlier general state space setting developed in [Tierney, Annals of Applied Probability, 1998] where the connection to Hamiltonian methods was more obscure. Altogether, the theoretical unity and reach of our main result provides a basis for deriving novel sampling algorithms while laying bare important relationships between existing methods.
