Robustness Properties for Simulations of Highly Reliable Systems
Bibliographic record
Abstract
Importance sampling (IS) is the primary technique for constructing reliable estimators in the context of rare-event simulation. The asymptotic robustness of IS estimators is often qualified by properties such as bounded relative error (BRE) and asymptotic optimality (AO). These properties guarantee that the estimator’s relative error remains bounded (or does not increase too fast) when the rare events becomes rarer. Other recently introduced characterizations of IS estimators are bounded normal approximation (BNA), bounded relative efficiency (BREff), and asymptotic good estimation of mean and variance. In this paper we introduce three additional property named bounded relative error of empirical variance (BREEV), bounded relative efficiency of empirical variance (BREffEV), and asymptotic optimality of empirical variance (AOEV), which state that the empirical variance has itself the BRE, BREff and AO property, respectively, as an estimator of the true variance. We then study the hierarchy between all these different characterizations for a model of highly-reliable Markovian systems (HRMS) where the goal is to estimate the failure probability of the system. In this setting, we show that BRE, BREff and AO are equivalent, that BREffEV, BREEV and AOEV are also equivalent, and that these two properties are strictly stronger than all other properties just mentioned. We also obtain a necessary and sufficient condition for BREEV in terms of quantities that can be readily verified from the parameters of the model.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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".