Variance estimation in integrated assessment models and its importance for hypothesis testing
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Variance in likelihood functions for multiple normally distributed data sets can be reliably estimated in integrated assessment models, and their values are important for accurate hypothesis tests. Commonly, assessment models are fitted to multiple types of observations by constructing a joint likelihood function that is then maximized. When a model contains no random effects and all random variables in the likelihood function represent errors in the prediction of measurements, then variances for each of the error distributions are estimable provided that no likelihood component has zero degrees of freedom. Theory for estimation of variances is reviewed. We show the relationship between concentrated likelihood based on the normal distribution and weighted least squares. Concentrated likelihood and weighted least squares are equivalent when the likelihood is made of normally distributed errors with constant variances, and the least squares weights are inversely proportional to the maximum likelihood estimates of the variances. A simulation study was made to show that variances and several output quantities are reasonably estimated for a herring-like population with moderate amounts of data. The simulation analysis and a case study with application to a herring population show that the choice of variances can strongly affect results of hypothesis tests.
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Direct model labels (unvalidated)
Per-model category and study-design labels from the labeling rounds. They are machine output, unvalidated, and the disagreement between models ships as data. No study design here is MEDLINE-validated yet.
| Model arm | Categories | Study design | Confidence |
|---|---|---|---|
| gpt | no category Domain: not available · Genre: Methods About the Canadian research system: no · About a Canadian topic: no | Simulation or modeling | high |
| grok | no category Domain: not available · Genre: Methods About the Canadian research system: no · About a Canadian topic: no | Simulation or modeling | high |
| opus | no category Domain: not available · Genre: Methods About the Canadian research system: no · About a Canadian topic: no | Simulation or modeling | high |
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 | 0.002 | 0.006 |
| 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) | 0.000 | 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