Bibliographic record
Abstract
Introduction In the examples in later chapters we use parametric models almost exclusively. These models are used to incorporate a key element of statistical thinking: the explicit recognition of uncertainty. In frequentist settings imprecise knowledge about the value of a single parameter is typically expressed through a collection of confidence intervals, or equivalently by computation of the P-values associated with a set of hypotheses. If prior information is available then Bayes' theorem can be employed to perform posterior inference. In almost every realistic setting, uncertainty is gauged using approximations, the most common of which rely on the application of the central limit theorem to quantities derived from the likelihood function. Not only does likelihood provide a powerful and very general framework for inference, but the resulting statements have many desirable properties. In this chapter we provide a brief overview of the main approximations for likelihood inference. We present both first order and higher order approximations; first order approximations are derived from limiting distributions, and higher order approximations are derived from further analysis of the limiting process. A minimal amount of theory is given to structure the discussion of the examples in Chapters 3 to 7; more detailed discussion of asymptotic theory is given in Chapter 8. Scalar parameter In the simplest situation, observations y 1 , …, y n are treated as a realization of independent identically distributed random variables Y 1 , …, Y n whose probability density function f ( y ; θ) depends on an unknown scalar parameter θ.
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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 | 0.003 | 0.014 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.014 | 0.004 |
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".