Scaling limits for the transient phase of local Metropolis–Hastings algorithms
Scaling limits for the transient phase of local Metropolis–Hastings algorithms
复制标题
本地 Metropolis-Hastings 算法瞬态阶段的缩放限制
DOI：
10.1111/j.1467-9868.2005.00500.x
复制
发表时间：
2005
期刊：
影响因子：
--
通讯作者：
J. Rosenthal
中科院分区：
文献类型：
--
作者：
O. F. Christensen;G. Roberts;J. Rosenthal
摘要。在其初始瞬态阶段，这些算法在较高的算法中考虑了高维的算法。瞬态相位是非常规律的 - 相反，算法的样本路径实际上类似于确定性轨迹，而langevin算法的方差为缩放为最佳范围。基于我们的理论实施的行为和实用指导的类型。
Summary. The paper considers high dimensional Metropolis and Langevin algorithms in their initial transient phase. In stationarity, these algorithms are well understood and it is now well known how to scale their proposal distribution variances. For the random‐walk Metropolis algorithm, convergence during the transient phase is extremely regular—to the extent that the algo‐rithm's sample path actually resembles a deterministic trajectory. In contrast, the Langevin algorithm with variance scaled to be optimal for stationarity performs rather erratically. We give weak convergence results which explain both of these types of behaviour and practical guidance on implementation based on our theory.