A Unified Framework for Multiple-Try Metropolis: Construction and Empirical Benchmarks
Bibliographic record
Abstract
The multiple-try Metropolis (MTM) algorithm uses a compound proposal with multiple candidate draws to improve local sampling efficiency. While several methodological works have continued to develop MTM and the multi-candidate mechanism that characterizes it, the literature lacks a unified comparison of these components. This paper presents a structured formulation of MTM within the involutive MCMC framework, providing a principled approach for deriving valid acceptance probabilities based on the proposal mechanism. Through a comprehensive simulation experiment, we evaluate the impact of MTM configurations on non-Gaussian and multimodal target distributions. Our results reveal that while weight functions are a focus of several methodological developments, their impact on stationary sampling efficiency is secondary to the configuration of the proposal distribution. Furthermore, we find that while increasing the number of candidates enhances per-iteration efficiency, the realized performance gains are offset by computational overhead introduced by multiple candidacy unless parallelize computing is used. Our findings offer practical guidance for configuring an MTM algorithm for complex and non-Gaussian targets.
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How this classification was reachedexpand
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 | 0.001 | 0.006 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".