A Differential Geometric Approach to Bayesian Marginalization
Why this work is in the frame
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Bibliographic record
Abstract
The statistical tool box offers a wide range of inference techniques to choose from; regrettably, the reliability of these methods in the sense of ‘reproducibility of frequency properties’ can often be unclear or even ignored. We examine this issue for default Bayes methods and develop a prior that leads to full second-order inference for any regular scalar parameter of interest in presence of nuisance parameters; the new prior is Jeffreys based. Also, in parallel, we show that such second-order accuracy is widely unavailable for vector parameters of interest through the Bayesian framework, unless the interest parameter has a special linearity. Detailed examples, including simulations, are presented and discussed.
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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) | 0.001 | 0.000 |
| Bibliometrics | 0.004 | 0.018 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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