Markov Chain Monte Carlo Approach for Parameter Uncertainty Quantification and Its Impact on Groundwater Mass Transport Modeling: Influence of Prior Distribution
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Bibliographic record
Abstract
Markov Chain Monte Carlo (MCMC) theory and stochastic simulation techniques were incorporated to analyze the effect of different prior knowledge on quantifying parameter uncertainty and its impact on mass transport in heterogeneous aquifer. The MCMC algorithm employing the Metropolis-Hastings rule (MH-MCMC) was used to obtain the posterior distribution of log-hydraulic conductivity. Random simulation technology, Sequential Gaussian Simulation, was used to generate a spatial stochastic hydraulic conductivity field. We investigated two different assumptive prior knowledge scenarios, a uniform prior distribution and a Gaussian prior distribution. Results showed that the prior knowledge could affect the posterior distributions of parameters. When the Gaussian prior distribution was adopted, there was a better convergence of parametric posterior distribution and a decrease in the zone of uncertainty influence and the area of confidence interval on groundwater mass transport modeling. However, it was difficult to draw the conclusion that the Gaussian prior distribution was preferred because the relative influence of parameter prior distribution depended on the location, number of measurements, and methods to reflect the heterogeneity of hydraulic conductivity. Therefore, the prior distribution is a sensitive input parameter and should be defined based upon best available data.
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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 | 0.000 |
| 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 | 0.000 |
| 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