Maximum likelihood inference for multivariate delay differential equation models
Bibliographic record
Abstract
The maximum likelihood inference framework for delay differential equation models in the multivariate settings is developed. The number of delay parameters is assumed to be one or more. This study does not make any restrictive assumptions on the form of the underlying delay differential equations which was one of the limitations of some of the previous work. Thus, the maximum likelihood inference framework can be applied to general delay differential equation models with multiple delay parameters. To obtain the maximum likelihood estimator and estimate of the information matrix, two numerical algorithms are developed: (i) the adaptive grid and (ii) the gradient descent algorithms. Two examples of multivariate delay differential equation models related to the epidemic and pharmacokinetic models, respectively, are presented in this paper. For the unknown parameters, standard errors and confidence intervals are constructed, and formulas and techniques for producing the information matrix are developed. The code and computations are developed with the help of the mathematical software MATLAB.
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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 | 0.005 |
| 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 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".