论文标题
使用两个投影理论对两个组件吉布斯采样器的分析
Analysis of two-component Gibbs samplers using the theory of two projections
论文作者
论文摘要
两个投影的理论用于研究两个组成的吉布斯采样器。通过这一理论，关于两组分Gibbs采样器的渐近方差的以前难以置信的问题被简化为基本基质代数练习。已经发现，从渐近方差方面，两组分组的随机弹药吉布斯采样器永远不会更糟，只要选择了选择概率，就可以比其确定性扫描的对应物好得多。当两个组件之间的计算成本差异很大时，尤其是这种情况。结果与已知的事实形成鲜明对比：确定性扫描版本具有更快的收敛速率，这也可以从本文的方法得出。另一方面，确定性 - 扫描采样器的修改版本，其计算成本可以优于随机扫描版本。
The theory of two projections is utilized to study two-component Gibbs samplers. Through this theory, previously intractable problems regarding the asymptotic variances of two-component Gibbs samplers are reduced to elementary matrix algebra exercises. It is found that in terms of asymptotic variance, the two-component random-scan Gibbs sampler is never much worse, and could be considerably better than its deterministic-scan counterpart, provided that the selection probability is appropriately chosen. This is especially the case when there is a large discrepancy in computation cost between the two components. The result contrasts with the known fact that the deterministic-scan version has a faster convergence rate, which can also be derived from the method herein. On the other hand, a modified version of the deterministic-scan sampler that accounts for computation cost can outperform the random-scan version.
