An Approximate Expectation Maximization Algorithm for Estimating Parameters, Noise Variances, and Stochastic Disturbance Intensities in Nonlinear Dynamic Models
Bibliographic record
Abstract
An algorithm is proposed for simultaneous estimation of model parameters, process disturbance intensities, and measurement noise variances for nonlinear dynamic systems that are described by stochastic differential equations. The proposed fully-Laplace approximation expectation maximization (FLAEM) algorithm uses an iterative approach wherein, in the first step, the model parameters are estimated using the approximate maximum likelihood estimation objective function developed by Varziri et al.,1 assuming that disturbance intensities and noise variances are known. In the second step, process disturbance intensities and measurement noise variance estimates are updated using expressions that rely on the fully-Laplace approximation in the expectation maximization algorithm. The proposed FLAEM method is illustrated using a nonlinear two-state continuous stirred tank reactor (CSTR) example. The effectiveness of the FLAEM algorithm is compared with a maximum-likelihood based method proposed by Kristensen et al.2 For the CSTR example studied, FLAEM provides more accurate parameter estimates and is more robust to poorly known initial guesses of parameters and to smaller data sets.
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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 | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".