HYPOTHESIS ASSESSMENT USING THE BAYES FACTOR AND RELATIVE BELIEF RATIO
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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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.087 | 0.287 |
| Meta-epidemiology (narrow) | 0.004 | 0.002 |
| Meta-epidemiology (broad) | 0.006 | 0.004 |
| Bibliometrics | 0.015 | 0.008 |
| Science and technology studies | 0.002 | 0.011 |
| Scholarly communication | 0.012 | 0.013 |
| Open science | 0.006 | 0.006 |
| Research integrity | 0.006 | 0.008 |
| Insufficient payload (model declined to judge) | 0.007 | 0.002 |
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 source (direct Gemma or distilled Codex), 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".