Optimal Sample Size Determination based on Bayesian Reliability and Value of Information
Bibliographic record
Abstract
In the structural reliability analysis, the probabilistic distributions of basic random variables may contain uncertainties arising from the imperfect knowledge from which the distributions are elicited. It subsequently introduces uncertainty into the calculated failure probability Pf, which may affect the decision-making. To reduce the uncertainty of the failure probability estimation, it is desirable to collect samples of the basic random variables and use these samples to update the corresponding probability distributions. In this work, the relationship between the sample size of the basic random variable and variance of the estimated failure probability is derived by using the Bayesian pre-posterior analysis, based on which the optimal sample size criterion is established. To make the pre-posterior analysis and criterion applicable to a wide range of distributions, continuous random variables are discretized at first. The probability mass functions of the discretized random variables are then assigned Dirichlet prior distributions. The total probability theorem is employed to express Pf in terms of PMFs of the discretized variables and conditional failure probabilities corresponding to given values of discretized variables. Then the prior, posterior and pre-posterior analysis of Pf are carried out. The optimal sample size criterion to maximize the expected net gain of sampling is developed based on the result of the pre-posterior analysis of Pf and quadratic loss function. An example of determining the optimal number of burst tests for collecting the samples of model error of the burst capacity model for corroded pipelines is used to illustrate the proposed criterion. Moreover, the sensitivity analysis indicates that the optimal sample size is insensitive to the discretization of the basic random variables, but sensitive to the equivalent sample size of the prior Dirichlet distribution.
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How this classification was reachedexpand
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 | 0.002 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.002 |
| Open science | 0.001 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".