Rare events, splitting, and quasi-Monte Carlo
Bibliographic record
Abstract
In the context of rare-event simulation, splitting and importance sampling (IS) are the primary approaches to make important rare events happen more frequently in a simulation and yet recover an unbiased estimator of the target performance measure, with much smaller variance than a straightforward Monte Carlo (MC) estimator. Randomized quasi-Monte Carlo (RQMC) is another class of methods for reducing the noise of simulation estimators, by sampling more evenly than with standard MC. It typically works well for simulations that depend mostly on very few random numbers. In splitting and IS, on the other hand, we often simulate Markov chains whose sample paths are a function of a long sequence of independent random numbers generated during the simulation. In this article, we show that RQMC can be used jointly with splitting and/or IS to construct better estimators than those obtained by either of these methods alone. We do that in a setting where the goal is to estimate the probability of reaching B before reaching (or returning to) A when starting A from a distinguished state not in B , where A and B are two disjoint subsets of the state space, and B is very rarely reached. This problem has several practical applications. The article is in fact a two-in-one: the first part provides a guided tour of splitting techniques, introducing along the way some improvements in the implementation of multilevel splitting. At the end of the article, we also give examples of situations where splitting is not effective. For these examples, we compare different ways of applying IS and combining it with RQMC.
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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 | 0.040 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.002 |
| 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".