Bayesian Prediction for the Gumbel Distribution Applied to Feeder Pipe Thicknesses
Bibliographic record
Abstract
This paper develops Bayesian prediction intervals for the minimum of any specified number of future measurements from a Gumbel distribution based on previous observations. The need for such intervals arises in the analysis of data from outlet side feeder pipes at Ontario nuclear power plants. The issue is how to best use these measurements in order to arrive at a statistically sound conclusion concerning the minimum thickness of all remaining uninspected pipes, in particular with what confidence can it be asserted that the remaining wall thicknesses are above an acceptable minimum to ensure a sufficiently high thickness up to the end of the next operating interval. The result gives a probability measure of the potential benefit of performing additional inspections when considered against the additional radiation exposure and the cost of performing additional inspections. Previously, this problem was approached by adapting a classical prediction interval that was originally derived for normal data. Here we examine both a hybrid Bayesian method that combines Bayesian ideas with maximum likelihood and also a full Bayesian approach using Markov Chain Monte Carlo. We show that the latter gives larger lower prediction limits and therefore more margin to fitness for service.
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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 | 0.012 | 0.054 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.002 | 0.003 |
| 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".