Optimal Scaling of Random Walk Metropolis algorithms with\nDiscontinuous target densities
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Bibliographic record
Abstract
We consider the optimal scaling problem for high-dimensional\nRandom walk Metropolis (RWM) algorithms where the target\ndistribution has a discontinuous probability density function. All\nprevious analysis has focused upon continuous target densities.\nThe main result is a weak convergence result as the dimensionality\n$d$ of the target densities converges to $\\infty$. In particular,\nwhen the proposal variance is scaled by $d^{-2}$, the sequence of\nstochastic processes formed by the first component of each Markov\nchain converges to an appropriate Langevin diffusion process.\nTherefore optimising the efficiency of the RWM algorithm is\nequivalent to maximising the speed of the limiting diffusion. This\nleads to an asymptotic optimal acceptance rate of $e^{-2}\n(=0.1353)$ under quite general conditions. The results have major\npractical implications for the implementation of RWM algorithms by\nhighlighting the detrimental effect of choosing RWM algorithms\nover Metropolis-within-Gibbs algorithms.
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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 | 0.002 | 0.000 |
| 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 | 0.000 |
| 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