A parametric Bayesian combination of local and regional information in flood frequency analysis
Bibliographic record
Abstract
Because of their impact on hydraulic structure design as well as on floodplain management, flood quantiles must be estimated with the highest precision given available information. If the site of interest has been monitored for a sufficiently long period (more than 30–40 years), at‐site frequency analysis can be used to estimate flood quantiles with a fair precision. Otherwise, regional estimation may be used to mitigate the lack of data, but local information is then ignored. A commonly used approach to combine at‐site and regional information is the linear empirical Bayes estimation: Under the assumption that both local and regional flood quantile estimators have a normal distribution, the empirical Bayesian estimator of the true quantile is the weighted average of both estimations. The weighting factor for each estimator is conversely proportional to its variance. We propose in this paper an alternative Bayesian method for combining local and regional information which provides the full probability density of quantiles and parameters. The application of the method is made with the generalized extreme values (GEV) distribution, but it can be extended to other types of extreme value distributions. In this method the prior distributions are obtained using a regional log linear regression model, and then local observations are used within a Markov chain Monte Carlo algorithm to infer the posterior distributions of parameters and quantiles. Unlike the empirical Bayesian approach the proposed method works even with a single local observation. It also relaxes the hypothesis of normality of the local quantiles probability distribution. The performance of the proposed methodology is compared to that of local, regional, and empirical Bayes estimators on three generated regional data sets with different statistical characteristics. The results show that (1) when the regional log linear model is unbiased, the proposed method gives better estimations of the GEV quantiles and parameters than the local, regional, and empirical Bayes estimators; (2) even when the regional log linear model displays a severe relative bias when estimating the quantiles, the proposed method still gives the best estimation of the GEV shape parameter and outperforms the other approaches on higher quantiles provided the relative bias is the same for all quantiles; and (3) the gain in performance with the new approach is considerable for sites with very short records.
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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 | 0.006 | 0.018 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.001 |
| 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".