Two convergence properties of hybrid samplers
Two convergence properties of hybrid samplers
复制标题
混合采样器的两个收敛特性
DOI：
10.1214/aoap/1028903533
复制
发表时间：
1998
影响因子：
1.8
通讯作者：
J. Rosenthal
中科院分区：
文献类型：
--
作者：
G. Roberts;J. Rosenthal
马尔可夫链蒙特卡罗（MCMC）算法的理论工作迄今主要集中在简单算法，如吉布斯采样器，或全维黑斯廷斯-大都会算法的性能。在实践中，这些简单的算法被用作更复杂方法的构建模块，我们将其称为混合采样器。通常希望良好的收敛性（几何遍历性等）。将意味着混合链的类似性质。然而，很少有人严格知道。在本文中，我们集中在两个特殊情况下的混合采样器。在第一种情况下，我们提供了一个定量的结果所产生的混合链的收敛速度。在第二种情况下，考虑到各种大都会算法的组合，我们建立了几何遍历性。
Theoretical work on Markov chain Monte Carlo (MCMC) algorithms has so far mainly concentrated on the properties of simple algorithms such as the Gibbs sampler, or the full-dimensional Hastings-Metropolis algorithm. In practice, these simple algorithms are used as building blocks for more sophisticated methods, which we shall refer to as hybrid samplers. It is often hoped that good convergence properties (geometric ergodicity, etc.) of the building blocks will imply similar properties of the hybrid chains. However, little is rigorously known. In this paper, we concentrate on two special cases of hybrid samplers. In the first case, we provide a quantitative result for the rate of convergence of the resulting hybrid chain. In the second case, concerning the combination of various Metropolis algorithms, we establish geometric ergodicity.