Likelihood Methods for Basic Stratified Sampling, with Application to Von Bertalanffy Growth Model Estimation
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Bibliographic record
Abstract
This paper mainly addresses maximum likelihood estimation for a response-selective stratified sampling scheme, the basic stratified sampling (BSS), in which the maximum subsample size in each stratum is fixed. We derived the complete-data likelihood for BSS, and extended it as a full-data likelihood by incorporating incomplete data. We also similarly extended the empirical proportion likelihood approach for consistent and efficient estimation. We conducted a simulation study to compare these two new approaches with the existing estimation methods in BSS. Our result indicates that they perform as well as the standard full information likelihood approach. Methods were illustrated using a growth model for fish size at age, including between-individual variability. One of our major conclusions is that the fully observed BSS data, the partially observed data used for stratification, and the sampling strategy are all important in constructing a consistent and efficient estimator.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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