Connections of a spectral nature are formed between Gibbs samplers and their blocked and collapsed variants. The solidarity principle of the spectral gap for full Gibbs samplers is generalized to different cycles and mixtures of Gibbs steps. This generalized solidarity principle is employed to establish that every cycle and mixture of Gibbs steps, which includes blocked Gibbs samplers and collapsed Gibbs samplers, inherits a spectral gap from a full Gibbs sampler. Exact relations between the spectra corresponding to blocked and collapsed variants of a Gibbs sampler are also established. An example is given to show that a blocked or collapsed Gibbs sampler does not in general inherit geometric ergodicity or a spectral gap from another blocked or collapsed Gibbs sampler.

翻译：本文建立了吉布斯采样器与其分块及折叠变体之间的谱性质联系。将全吉布斯采样器的谱隙团结性原理推广至不同的循环及吉布斯步骤混合情形。利用该推广的团结性原理，证明了包含分块吉布斯采样器与折叠吉布斯采样器在内的任何吉布斯步骤循环与混合，均可从全吉布斯采样器继承谱隙。同时确立了吉布斯采样器的分块与折叠变体对应谱之间的精确关系。文中给出示例表明，分块或折叠吉布斯采样器通常无法从另一分块或折叠吉布斯采样器继承几何遍历性或谱隙。