On the maximum likelihood estimation based on one-shot test device data and the associated adaptive design
Bibliographic record
Abstract
In this paper, we develop iterative methods to estimate parameters based on one-shot device test data using maximum likelihood estimation (MLE) for parametric, semi-parametric and non-parametric models. The EM-algorithm has been widely used to obtain the MLE in a variety of situations. But, the discussion on the direct Newton-Raphson algorithm seems to be scarce. To fill this gap, we develop the iterative method based on the Newton-Raphson algorithm and the method of scoring, which could be used in many commonly used reliability models. We also suggest a method for obtaining initial values under different model assumptions. The derived information matrix is further used for the optimal adaptive design, a topic that has not been studied much. Monte Carlo simulation studies reveal that the proposed method converges quickly and that the initial values obtained through the proposed least-square method are quite close to the MLE and leads to faster convergence in turn, particularly with large samples. Finally, two datasets from the literature are used to demonstrate all the methods developed here.
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How this classification was reachedexpand
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 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".