Bibliographic record
Abstract
The ordinary differential equation (ODE) models are prominent to characterize the mechanism of dynamical systems with various applications in biology, engineering, and many other areas. While the form of ODE models is often proposed based on the understanding or assumption of the dynamical systems, the values of ODE model parameters are often unknown. Hence, it is of great interest to estimate the ODE parameters once the observations of dynamic systems become available. The parameter cascade method initially proposed by [@parcascade] is shown to provide an accurate estimation of ODE parameters from the noisy observations at a low computational cost. This method is further promoted with the implementation in the R package CollocInfer by [@CollocInfer]. However, one bottleneck in using CollocInfer to implement the parameter cascade method is the tedious derivations and coding of the Jacobian and Hessian matrices required by the objective functions for doing estimation. We develop an R package pCODE to implement the parameter cascade method, which has the advantage that the users are not required to provide any Jacobian or Hessian matrices. Functions in the pCODE package accommodate users for estimating ODE parameters along with their variances and tuning the smoothing parameters. The package is demonstrated and assessed with four simulation examples with various settings. We show that pCODE offers a derivative-free procedure to estimate any ODE models where its functions are easy to understand and apply. Furthermore, the package has an online Shiny app at <https://pcode.shinyapps.io/pcode/>.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.021 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.010 | 0.005 |
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 source (direct Gemma or distilled Codex), 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".