On quasi‐likelihood estimation for branching processes with immigration
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Bibliographic record
Abstract
Abstract In the theory of estimation for branching processes it is well known that, in the super‐critical case, the so‐called conditional least‐squares and the conditional weighted least‐squares methods may not yield unbiased and hence consistent estimates for the mean parameters of the offspring and immigration distributions. In this paper, the authors propose a new conditional quasi‐likelihood method in the context of negative binomial offspring and immigration distributions that provides mean estimates with smaller mean squared errors in the super‐critical case as compared to the previous approaches. Further, they simplify the conditional quasi‐likelihood estimating equations both for the mean and the variance parameters under a special model with binary offspring distribution appropriate for a controlled population. It is also demonstrated empirically that a reasonable estimate for the variance or overdispersion parameter requires that the data be collected over a long period of time. The Canadian Journal of Statistics 38: 290–313; 2010 © 2010 Statistical Society of Canada
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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 | 0.000 | 0.009 |
| 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