Generalized Importance Sampling for Nested Simulation
Bibliographic record
Abstract
Importance sampling (IS) is a classical variance reduction technique. Under mild conditions, an IS estimator is unbiased, so one often seeks the variance-minimizing optimal sampling distribution. IS has remarkable success in many applications, such as engineering, operations research, and finance. In some applications, such as enterprise risk management and input uncertainty quantification, complex simulation designs, such as nested simulation, arise naturally. The outer-level simulation generates a set of risk factors, i.e., the scenarios, which are used as inputs for inner-level simulations. Nested simulation leads to wasteful use of computations, as inner simulation outputs in each scenario are isolated from other scenarios. In this study, we propose, analyze, and test a generalized importance sampling technique for nested simulation. Our generalized IS approach reuses one set of inner simulation outputs across different outer scenarios. Numerical experiments show that our proposal is orders of magnitude more efficient than the standard procedure.
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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 | 0.000 | 0.001 |
| 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".