Probabilistic Evaluation of Causal Relationship between Variables for Water Quality Management
Bibliographic record
Abstract
In aquatic environments, a complex interplay exists among physical, chemical, and biological water quality characteristics, which are constantly influenced by exogenous factors such as hydrological, meteorological and geological conditions. Due to the spatial and temporal variations of exogenous factors, the relationship between the water quality parameters and these factors hence becomes complicated and challenging. Given the large data matrix, one type of methods frequently seen in the literature belongs to the multivariate analysis which generates a qualitative measure of the relationships among variables in a geometrically intuitive way. However, a quantitative evaluation from a probabilistic perspective is favorable since it defines a measurable causality among variables so that more efficient water management strategies can be formulated. This paper illustrates a new way to discover the relationship between two variables by estimating their joint distribution which fully interprets the statistical dependence. A multivariate Gaussian mixture model was employed to describe the data. The model parameters were determined using the previously developed estimation approach, which is capable of dealing with both multivariate variables and censored data. The joint distribution and the conditional distribution were computed and used to describe the statistical distribution of water quality parameters, which are subject to the effects of hydro-meteorological conditions. The method was demonstrated by a case study on the Bow River in Alberta, Canada. The results shed light on how one variable affects the distribution of the other variable under complex environments in a probabilistic context.
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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 | 0.008 | 0.028 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".