Quasi-random numbers and their applications: using lattice rules for variance reduction in simulation
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Bibliographic record
Abstract
Quasi-Monte Carlo methods are designed to improve upon the Monte Carlo method for multidimensional numerical integration by using a more regularly distributed point set than the i.i.d. sample associated with Monte Carlo. Lattice rules are one family of quasi-Monte Carlo methods, originally proposed by Korobov in 1959. In this paper, we explain how randomized lattice rules can be used to construct efficient estimators for typical simulation problems, and we give several numerical examples. We are interested in two main aspects: Studying the variance of these estimators and finding which properties of the lattice rules should be considered when defining a selection criterion to rate and choose them. Our numerical results for three different problems illustrate how this methodology typically improves upon the usual Monte Carlo simulation method.
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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 | 0.000 | 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) | 0.001 | 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 it