A Bayesian perspective on input uncertainty in model calibration: Application to hydrological model “abc”
Bibliographic record
Abstract
The impact of input errors in the calibration of watershed models is a recurrent theme in the water science literature. It is now acknowledged that hydrological models are sensitive to errors in the measures of precipitation and that those errors bias the model parameters estimated via the standard least squares (SLS) approach. This paper presents a Bayesian uncertainty framework allowing one to account for input, output, and structural (model) uncertainties in the calibration of a model. Using this framework, we study the impact of input uncertainty on the parameters of the hydrological model “abc.” Mostly of academic interest, the “abc” model has a response linear to its input, allowing the closed form integration of nuisance variables under proper assumptions. Using those analytical solutions to compute the posterior density of the model parameters, some interesting observations can be made about their sensitivity to input errors. We provide an explanation for the bias identified in the SLS approach and show that in the input error context the prior on the input “true” value has a significant influence on the parameters' posterior density. Overall, the parameters obtained from the Bayesian method are more accurate, and the uncertainty over them is more realistic than with SLS. This method, however, is specific to linear models, while most hydrological models display strong nonlinearities. Further research is thus needed to demonstrate the applicability of the uncertainty framework to commonly used hydrological models.
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How this classification was reachedexpand
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 | 0.000 |
| 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 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".