Hierarchical Bayesian modelling of geotechnical data: application to rock strength
Bibliographic record
Abstract
With the introduction and revisions of geotechnical limit states design (LSD) standards such as Eurocode 7, rock engineering design is moving towards reliability-based design, a method for which statistical characterisation of design parameters is essential. However, the often limited project-specific data in rock engineering do not allow straightforward application of classical statistical analyses, and thus alternative approaches are required. In this paper, hierarchical Bayesian modelling is first introduced as a means of logically combining data from different sources to augment limited project-specific data. A Bayesian hierarchical non-linear regression model for the analysis of rock strength data is then developed and implemented; it is applied to 40 strength data sets of granite retrieved from the literature. In the context of these data, the advantages of the hierarchical model and the improvements in strength parameter estimations brought about by its application are discussed. Also discussed is the goodness-of-fit of the hierarchical model in comparison with more conventional statistical models. The paper concludes with suggestions for further development of the proposed hierarchical model, and the potential of hierarchical modelling as a general approach to statistical modelling of geotechnical data.
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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 | 0.009 | 0.033 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".