A Note on Convergence of the Equi-Energy Sampler
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Bibliographic record
Abstract
Abstract In a recent article, ‘The equi-energy sampler with applications statistical inference and statistical mechanics' [Ann. Stat., 34 (2006) 1581–1619], Kou, Zhou, and Wong presented a new stochastic simulation method called the equi-energy (EE) sampler. This technique is designed to simulate from a probability measure π, perhaps only known up to a normalizing constant. The authors demonstrate that the sampler performs well in quite challenging problems but their convergence results (Theorem 2) appear incomplete. This was pointed out, in the discussion of the article, by Atchadé and Liu [3 Atchadé , Y. , and Liu , J.S. 2006 . Discussion of Kou, Zhou and Wong . Ann. Statist. 34 : 1620 – 1628 .[Crossref] , [Google Scholar]] who proposed an alternative convergence proof. However, this alternative proof, whilst theoretically correct, does not correspond to the algorithm that is implemented. In this note we provide a new proof of convergence of the equi-energy sampler based on the Poisson equation and on the theory developed in Andrieu et al. [2 Andrieu , C. , Jasra , A. , Doucet , A. , and Del Moral , P. 2007 . Non-linear Markov chain Monte Carlo via self interacting approximations . Technical Report , University of Bristol . [Google Scholar]] for non linear Markov chain Monte Carlo (MCMC). The objective of this note is to provide a proof of correctness of the EE sampler when there is only one feeding chain; the general case requires a much more technical approach than is suitable for a short note. In addition, we also seek to highlight the difficulties associated with the analysis of this type of algorithm and present the main techniques that may be adopted to prove the convergence of it.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it