Confidence Intervals for Randomized Quasi-Monte Carlo Estimators
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Bibliographic record
Abstract
Randomized Quasi-Monte Carlo (RQMC) methods provide unbiased estimators whose variance often converges at a faster rate than standard Monte Carlo as a function of the sample size. However, computing valid confidence intervals is challenging because the observations from a single randomization are dependent and the central limit theorem does not ordinarily apply. A natural solution is to replicate the RQMC process independently a small number of times to estimate the variance and use a standard confidence interval based on a normal or Student t distribution. We investigate the standard Student t approach and two bootstrap methods for getting nonparametric confidence intervals for the mean using a modest number of replicates. Our main conclusion is that intervals based on the Student t distribution are more reliable than even the bootstrap t method on the integration problems arising from RQMC.
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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 | 0.002 | 0.007 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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