Bayesian and subset-selection methods for parameter estimation in mechanistic models with limited data: A review and comparison
Bibliographic record
Abstract
Parameters in mathematical models require accurate estimation for the model to give reliable predictions. When data are limited, weighted least-squares methods sometimes result in unreliable parameter estimates. Two popular approaches to combat this issue are subset-selection and Bayesian estimation. Subset-selection ranks model parameters from most- to least-estimable based on prior parameter knowledge and available data. The ranked list is used to determine which parameters should be estimated, and which should be fixed at initial guesses to avoid overfitting. Bayesian estimation methods summarize prior knowledge about parameters using probability distributions. Simple Bayesian methods result in objective functions with penalty terms that keep parameter estimates near their initial guesses unless there is considerable information in the data. Subset-selection and Bayesian methods result in different parameter estimates using the same data and similar prior information. A hydroisomerization case study is presented comparing the merits and shortcoming of each approach. Bayesian estimation is preferred if prior parameter knowledge is reliable, but provides misleading results when the modeler is overly confident about poor parameter guesses. Subset-selection methods are more computationally expensive, less susceptible to problems arising from poor initial guesses, and provide additional information about influences of model parameters and opportunities for model simplification. • Models require accurate parameter estimates to be useful • Estimating model parameters with limited data can cause major difficulties • Bayesian and subset-selection methods alleviate these issues • A literature review is conducted on these two estimation methods • A comprehensive case study compares their merits and shortcomings
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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 | 0.009 | 0.019 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.004 | 0.004 |
| Bibliometrics | 0.006 | 0.008 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.004 | 0.001 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 0.002 |
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".