Bayesian parameter estimation using truncated normal distributions as priors for parameters in fundamental models of chemical processes
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Bibliographic record
Abstract
Abstract Modellers of chemical processes with knowledge about plausible parameter values use Bayesian parameter estimation methods to account for their prior beliefs. Some modellers specify prior distributions with finite parameter ranges, such as uniform distributions and truncated normal distributions, because they better account for knowledge about realistic parameter ranges than normal prior distributions with parameter values ranging between and . We derive closed‐form objective functions for Bayesian parameter estimation with truncated normal priors and uniform priors, for the first time, so that parameter estimation can be performed by solving simple optimization problems rather than using complex sampling‐based techniques. A parametric bootstrapping method that considers truncated normal priors and model nonlinearity is proposed to determine 95% confidence intervals and joint confidence regions. A pharmaceutical case study is used to show the effectiveness of the proposed objective functions and bootstrapping methodology. Confidence regions from bootstrapping are similar to linearization‐based confidence regions that do not account for truncation when truncated areas in normal prior distributions are relatively small. More truncation, which corresponds to more‐precise prior knowledge about the parameters, results in smaller joint confidence regions. The proposed methods will be attractive for parameter estimation in complex process models because they can be less computationally intensive than Markov chain Monte Carlo methods that provide similar results.
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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 | 0.007 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| 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