Improving confidence intervals and central value estimation in small datasets through hybrid parametric bootstrapping
Bibliographic record
Abstract
We developed a hybrid parametric bootstrapping (HPB) method for analyzing small datasets with high precision. This method addresses the challenge of estimating confidence intervals (CI) and central values when traditional distribution assumptions do not apply. Our HPB is combined with Steiner's Most Frequent Value (MFV) technique. The MFV method minimizes the information loss associated with small datasets, while the HPB considers the uncertainty of each separate element. As a practical example, we applied this innovative and robust statistical methodology to refine prior measurements of the half-life of Ru 97 . Using the MFV technique integrated with the HPB method, we obtained a significantly more precise half-life estimate, T 1 / 2 , MFV(HPB) = 2.8385 − 0.0075 + 0.0022 days. This refined value features a 68.27% confidence interval from 2.8310 to 2.8407 days and a 95.45% confidence interval from 2.8036 to 2.8485 days, as calculated using the percentile method. Our analysis demonstrates a substantial reduction in uncertainty–over 30 times lower than that reported in nuclear data sheets–indicating the potential for widespread analytical impact. In addition, employing alternative minimization strategies can reduce the statistical uncertainty by a further 44%. The HPB method effectively addresses the uncertainties inherent in small datasets, as demonstrated by re-evaluating the specific activity measurements for Ar 39 using underground data. We report S A MFV(HPB) = 0.966 − 0.020 + 0.027 Bq/kg atmAr , with confidence intervals (68.27%: 0.946–0.993; 95.45%: 0.921–1.029) derived using the percentile method. Advances in statistical methods are important for making data analysis more accurate and reliable, especially when combining and interpreting information from different sources. The developed tools help handle complex data more effectively, thereby improving the process and understanding of information in real-world applications where precision is essential. • Developed the Hybrid Parametric Bootstrapping (HPB) method for small datasets. • The Most Frequent Value (MFV) minimizes information loss and resists outliers. • HPB considers data-point uncertainties without assuming a specific distribution. • HPB does not assume data distribution, unlike standard parametric bootstrapping. • HPB and MFV were applied to evaluate the Ru-97 half-life. • HPB and MFV were used to re-evaluate the Ar-39 specific activity.
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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 | 0.043 | 0.267 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.005 | 0.005 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.004 | 0.006 |
| Open science | 0.006 | 0.006 |
| Research integrity | 0.003 | 0.006 |
| 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".