Hierarchical Bayesian Estimation of a Stochastic Plateau Response Function: Determining Optimal Levels of Nitrogen Fertilization
Bibliographic record
Abstract
Abstract This article seeks to determine the optimal level of nitrogen to apply to winter wheat. The article makes two methodological contributions. One is to extend the estimation of a stochastic plateau function to the case where the plateau has a beta distribution instead of a normal distribution. The second is to adapt hierarchical Bayesian methods as an alternative to the frequentist approach to estimate wheat yield response to nitrogen fertilizer. The economically optimal rate of nitrogen varies between 64 and 169 kg/ha and is consistently higher with the Bayesian method and higher under most scenarios when nonnormality is assumed for the plateau parameter. Based on the likelihood odds ratio, the normal distribution is preferred with maximum likelihood estimation. But, based on the deviance information criterion, the beta model is preferred with the Bayesian estimation. Cet article a pour objectif de déterminer le niveau optimal d'azote à appliquer au blé d'hiver. L'article apporte deux contributions méthodologiques. L'un consiste à étendre l'estimation d'une fonction de plateau stochastique au cas où le plateau a une distribution bêta au lieu d'une distribution normale. La seconde consiste à adapter les méthodes bayésiennes hiérarchiques comme alternative à l'approche classique pour estimer la réponse du rendement du blé à l'engrais azoté. Le taux d'azote économiquement optimal varie entre 64 kg ha‐1 et 169 kg ha‐1 et est toujours plus élevé avec la méthode bayésienne et plus élevé dans la plupart des scénarios lorsque la non‐normalité est supposée pour le paramètre plateau. Selon le rapport de probabilité, la distribution normale est préférée avec l'estimation du maximum de vraisemblance. Mais, en fonction du critère d'information de déviance, le modèle bêta est préféré en utilisant la méthode d'estimation bayésienne.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".