Bayesian estimation of ordinary differential equation models when the likelihood has multiple local modes
Why this work is in the frame
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Bibliographic record
Abstract
Abstract Ordinary differential equations (ODEs) are popularly used to model complex dynamic systems by scientists; however, the parameters in ODE models are often unknown and have to be inferred from noisy measurements of the dynamic system. One conventional method is to maximize the likelihood function, but the likelihood function often has many local modes due to the complexity of ODEs, which makes the optimizing algorithm be vulnerable to trap in local modes. In this paper, we solve the global optimization issue of ODE parameters with the help of the Stochastic Approximation Monte Carlo (SAMC) algorithm which is shown to be self-adjusted and escape efficiently from the “local-trapping” problem. Our simulation studies indicate that the SAMC method is a powerful tool to estimate ODE parameters globally. The efficiency of SAMC method is demonstrated by estimating a predator-prey ODEs model from real experimental data.
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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 | 0.001 | 0.001 |
| 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