On the Behaviour of D-Optimal Exact Designs Under Changing Regression Polynomials
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Bibliographic record
Abstract
The behaviour of D-optimal exact designs for first order polynomial models under changing regression polynomials is considered. The polynomials, some of which are with or without intercept or with or without interactive term, are defined on design regions that are supported by the points of the Circumscribed Central Composite Design. The best N-point D-optimal exact design for the intercept model (model 1), is the same as the best N-point D-optimal design for the no-intercept model (model 3). Similarly, the best N-point D-optimal design for the intercept model (model 2) is the same as the best N-point D-optimal design for the no-intercept model (model 4), as measured by the determinant values, D-efficiencies, G-efficiencies and Condition numbers. Other N-point designs constructed using the no-intercept models had better determinant values than their corresponding intercept models. The condition numbers indicate that for model 1, the 4-point D-optimal design is orthogonal. For model 2, the 2-point D-optimal exact design and the 4-point D-optimal exact designs are orthogonal. For model 3, the 4-point D-optimal exact design is orthogonal and for model 4, the 4-point D-optimal exact design is orthogonal. Other N-sized designs show less orthogonality. The Equivalence of D-optimality and G-optimality criteria is established for the 4-point design under model 1, for the 2-point and 4-point designs under model 2, for the 4-point design under model 3 and for the 4-point design under model 4.
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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 | 0.008 | 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 | 0.001 | 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