论文标题
两分量MCMC采样器的收敛速率
Convergence Rates of Two-Component MCMC Samplers
论文作者
论文摘要
组件的MCMC算法，包括吉布斯和有条件的大都市 - 杂物采样器，通常用于从多元概率分布中抽样。关于Gibbs算法的一个长期存在的问题是，确定性扫描（系统扫描）采样器的收敛速度是否比其随机扫描对应物更快。当采样器涉及两个组件时，我们通过建立两个采样器的$ l^2 $收敛速率之间的确切定量关系来回答这个问题。该关系表明确定性扫描采样器收敛速度更快。我们还建立了两组分Gibbs采样器的收敛速率和某些有条件的大都市危机变体之间的定性关系。例如，可以表明，如果某些两个组件有条件的大都市束缚采样器在几何上是千古的，那么相关的吉布斯采样器也是如此。
Component-wise MCMC algorithms, including Gibbs and conditional Metropolis-Hastings samplers, are commonly used for sampling from multivariate probability distributions. A long-standing question regarding Gibbs algorithms is whether a deterministic-scan (systematic-scan) sampler converges faster than its random-scan counterpart. We answer this question when the samplers involve two components by establishing an exact quantitative relationship between the $L^2$ convergence rates of the two samplers. The relationship shows that the deterministic-scan sampler converges faster. We also establish qualitative relations among the convergence rates of two-component Gibbs samplers and some conditional Metropolis-Hastings variants. For instance, it is shown that if some two-component conditional Metropolis-Hastings samplers are geometrically ergodic, then so are the associated Gibbs samplers.
