Mixing and hitting times for Gibbs samplers and other non-Feller processes
Bibliographic record
Abstract
The hitting and mixing times are two often-studied quantities associated with Markov chains. Yuval Peres, Perla Sousi and Roberto Oliveira showed that the mixing times and “worst-case” hitting times of reversible Markov chains on finite state spaces are “equivalent”—that is, equal up to some universal multiplicative constant. We have extended this strong connection between mixing and hitting times to Markov chains satisfying the strong Feller property in an earlier work. In the present paper, we further extend the results to include Metropolis–Hastings chains, the popular Gibbs sampler (from statistics), and Glauber dynamics (from statistical physics), which make “one-dimensional” updates and thus do not satisfy the strong Feller property. We also apply this result to obtain decomposition bounds for such Markov chains. Our main tools come from nonstandard analysis.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.014 | 0.067 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.005 | 0.003 |
| Science and technology studies | 0.002 | 0.008 |
| Scholarly communication | 0.004 | 0.009 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.003 | 0.006 |
| Insufficient payload (model declined to judge) | 0.007 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".