Three enigmatic examples and inference from likelihood
Bibliographic record
Abstract
Abstract Statistics has many inference procedures for examining a model with data to obtain information concerning the value of a parameter of interest. If these give different results for the same model and data, one can reasonably want a satisfactory explanation. Over the last eighty years, three very simple examples have appeared intermittently in the literature, often with contradictory or misleading results; these enigmatic examples come from Cox, Behrens, and Box & Cox. The procedures in some generality begin with an observed likelihood function, which is known to provide just first order accuracy unless there is additional information that calibrates the parameter. In particular, default Bayes analysis seeks such calibration in the form of a model‐based prior; such a prior with second order accuracy is examined for the Behrens problem, but none seems available for the Box and Cox problem. Alternatively, higher‐order likelihood theory obtains such information by examining likelihood at and near the data and achieves third order accuracy. We examine both Bayesian and frequentist procedures in the context of the three enigmatic examples; simulations support the indicated accuracies. The Canadian Journal of Statistics © 2009 Statistical Society of Canada
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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 | 0.027 | 0.132 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.004 |
| Science and technology studies | 0.004 | 0.025 |
| Scholarly communication | 0.005 | 0.012 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.007 | 0.010 |
| 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".