Hua Xia, Kou S C
Department of Mathematics, Massachusetts Institute of Technology.
Stat Sin. 2011 Oct 1;21(4):1687-1711. doi: 10.5705/ss.2009.282.
We provide a complete proof of the convergence of a recently developed sampling algorithm called the equi-energy (EE) sampler (Kou, Zhou, and Wong, 2006) in the case that the state space is countable. We show that in a countable state space, each sampling chain in the EE sampler is strongly ergodic a.s. with the desired steady-state distribution. Furthermore, all chains satisfy the individual ergodic property. We apply the EE sampler to the Ising model to test its efficiency, comparing it with the Metropolis algorithm and the parallel tempering algorithm. We observe that the dynamic exponent of the EE sampler is significantly smaller than those of parallel tempering and the Metropolis algorithm, demonstrating the high efficiency of the EE sampler.
我们给出了一种最近开发的名为等能量（EE）采样器（Kou、Zhou和Wong，2006）的采样算法在状态空间可数情况下收敛性的完整证明。我们表明，在可数状态空间中，EE采样器中的每个采样链几乎必然是强遍历的，具有所需的稳态分布。此外，所有链都满足个体遍历性质。我们将EE采样器应用于伊辛模型以测试其效率，并将其与 metropolis算法和并行回火算法进行比较。我们观察到，EE采样器的动态指数明显小于并行回火算法和 metropolis算法的动态指数，这表明了EE采样器的高效率。
