A cluster‐sample approach for Monte Carlo integration using multiple samplers
Bibliographic record
Abstract
Abstract A computational problem in many fields is to estimate simultaneously multiple integrals and expectations, assuming that the data are generated by some Monte Carlo algorithm. Consider two scenarios in which draws are simulated from multiple distributions but the normalizing constants of those distributions may be known or unknown. For each scenario, existing estimators can be classified as using individual samples separately or using all the samples jointly. The latter pooled‐sample estimators are statistically more efficient but computationally more costly to evaluate than the separate‐sample estimators. We develop a cluster‐sample approach to obtain computationally effective estimators, after draws are generated for each scenario. We divide all the samples into mutually exclusive clusters and combine samples from each cluster separately. Furthermore, we exploit a relationship between estimators based on samples from different clusters to achieve variance reduction. The resulting estimators, compared with the pooled‐sample estimators, typically yield similar statistical efficiency but have reduced computational cost. We illustrate the value of the new approach by two examples for an Ising model and a censored Gaussian random field. The Canadian Journal of Statistics 41: 151–173; 2013 © 2012 Statistical Society of Canada
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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 | 0.013 | 0.046 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.005 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.007 | 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".