Tutorial: Guide to error propagation for particle counting measurements
Why this work is in the frame
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Bibliographic record
Abstract
Forward error propagation is an established technique for uncertainty quantification (UQ). This article covers practical applications of forward error propagation in the context of particle counting measurements. We begin by presenting pertinent error models, including the Poisson noise model, and assess their role in UQ. Next, we describe several basic techniques for UQ, including Gauss’s formula, its generalization to the Law of Propagation of Uncertainty (LPU), and the use of Monte Carlo (MC) sampling. We conclude with demonstrations of increasing complexity, including total number concentration, total mass concentration, penetration, and mass-based filtration efficiency scenarios. These examples serve two functions: (1) providing examples in which theoretical concepts are practically applied to interpret particle counting data and (2) presenting expressions that can be used to compute uncertainties for specific problems in particle counting measurement.
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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 | 0.003 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 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 it