Two Metropolis-Hastings algorithms for posterior measures with\n non-Gaussian priors in infinite dimensions
Bibliographic record
Abstract
We introduce two classes of Metropolis-Hastings algorithms for sampling\ntarget measures that are absolutely continuous with respect to non-Gaussian\nprior measures on infinite-dimensional Hilbert spaces. In particular, we focus\non certain classes of prior measures for which prior-reversible proposal\nkernels of the autoregressive type can be designed. We then use these proposal\nkernels to design algorithms that satisfy detailed balance with respect to the\ntarget measures. Afterwards, we introduce a new class of prior measures, called\nthe Bessel-K priors, as a generalization of the gamma distribution to measures\nin infinite dimensions. The Bessel-K priors interpolate between well-known\npriors such as the gamma distribution and Besov priors and can model sparse or\ncompressible parameters. We present concrete instances of our algorithms for\nthe Bessel-K priors in the context of numerical examples in density estimation,\nfinite-dimensional denoising and deconvolution on the circle.\n
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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 | 0.001 |
| 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 | 0.001 | 0.001 |
| Research integrity | 0.000 | 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".