Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.06745 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911366290341888 |
|---|---|
| author | Mak, Xavier Hobert, James P. |
| author_facet | Mak, Xavier Hobert, James P. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_06745 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Extensions of the solidarity principle of the spectral gap for Gibbs samplers to their blocked and collapsed variants Mak, Xavier Hobert, James P. Computation Probability Statistics Theory 60J05 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. |
| title | Extensions of the solidarity principle of the spectral gap for Gibbs samplers to their blocked and collapsed variants |
| topic | Computation Probability Statistics Theory 60J05 |
| url | https://arxiv.org/abs/2601.06745 |