Bayesian and frequentist inference derived from evidentiary first principles with applications to propagating uncertainty about statistical methods
Bibliographic record
Abstract
Unquantified uncertainty about probabilistic model assumptions tends to inflate claims of statistical significance, potentially leading to reported results that cannot be replicated. The same bias occurs at a higher level when Bayesian inference or frequentist inference is chosen to achieve significance in the absence of a way to propagate the uncertainty about which statistical paradigm to select. The objective of this article is to correct that bias at both levels on the basis of evidentiary first principles for statistical inference. It is found that just as Bayesian inference is warranted when a prior distribution is considered alongside the data as evidence, frequentist inference in the form of confidence intervals and their generalization to confidence distributions is warranted when a hypothesis testing procedure is considered as a piece of evidence. Hierarchical evidence in the same framework enables reporting results reflecting uncertainty about which of those pieces of evidence to admit as well as uncertainty about model assumptions. Practical results include a method of averaging Bayesian hypothesis testing with frequentist hypothesis testing and a method of averaging confidence intervals and/or credible intervals.
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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 | 0.046 | 0.181 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.006 | 0.004 |
| Science and technology studies | 0.002 | 0.010 |
| Scholarly communication | 0.006 | 0.009 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.003 | 0.009 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".