HYPOTHESIS ASSESSMENT USING THE BAYES FACTOR AND RELATIVE BELIEF RATIO
Why this work is in the frame
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Bibliographic record
Abstract
The Bayes factor is commonly used for assessing the evidence for or against a given hypothesis H0: θ ∈ Θ0, where Θ0 is a subset of the parameter space. In this paper we discuss the Bayes factor and various issues associated with its use. A Bayes factor is seen to be intimately connected with a relative belief ratio which provides a somewhat simpler approach to assessing the evidence in favor of H0. It is noted that, when there is a parameter of interest generating H0, then a Bayes factor for H0 can be defined as a limit and there is no need to introduce a discrete prior mass for Θ0 or a prior within Θ0. It is further noted that when a prior on Θ0 does not correspond to a conditional prior induced by a parameter of interest generating H0, then there is an inconsistency in prior assignments. This inconsistency can be avoided by choosing a parameter of interest that generates the hypothesis. A natural choice of a parameter of interest is given by a measure of distance of the model parameter from Θ0. This leads to a Bayes factor for H0 that is comparing the concentration of the posterior about Θ0 with the concentration of the prior about Θ0. The issue of calibrating a Bayes factor is also discussed and is seen to be equivalent to computing a posterior probability that measures the reliability of the evidence provided by the Bayes factor.
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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 | 0.000 |
| 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) | 0.002 | 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