Probabilistic estimation of specific surface area and cation exchange capacity: a global multivariate distribution
Bibliographic record
Abstract
Specific surface area (SSA) and cation exchange capacity (CEC) are two fundamental clay properties. However, the determination of CEC and SSA is challenging due to inherent uncertainties and difficulty in experimental measurement. A popular approach is to employ transformation models for their estimation. However, most of the existing models were developed on limited sample sizes and quantification of uncertainty associated with the estimate is not possible. Therefore, this study proposes a multivariate probabilistic approach for estimation of CEC and SSA. First, a five-dimensional database (278 × 5) for the parameters liquid limit (LL), plasticity index (PI), clay fraction (CF), CEC, and SSA (labelled as CLAY/C-S/5/278) is developed. Thereafter, multivariate distribution for the five parameters in the database is constructed using the vine copula approach. Implementation of the proposed approach is demonstrated by updating the prior–unconditional probability density functions (PDFs) of CEC and SSA given single or multiple clay parameters using Bayes’ rule. The posterior or conditional PDFs of CEC and SSA are also summarized as practitioner-friendly analytical expressions. Two geotechnical application examples are shown as well. In the proposed approach, CEC and SSA are characterized by their complete joint distribution and therefore this approach is superior to the popular deterministic transformation approach in literature.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| 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".