Uncertainty calculations for the measurement of<i>in vivo</i>bone lead by x-ray fluorescence
Bibliographic record
Abstract
In order to quantify the bone lead concentration from an in vivo x-ray fluorescence measurement, typically two estimates of the lead concentration are determined by comparing the normalized x-ray peak amplitudes from the Kalpha(1) and Kbeta(1) features to those of the calibration phantoms. In each case, the normalization consists of taking the ratio of the x-ray peak amplitude to the amplitude of the coherently scattered photon peak in the spectrum. These two Pb concentration estimates are then used to determine the weighted mean lead concentration of that sample. In calculating the uncertainties of these measurements, it is important to include any covariance terms where appropriate. When determining the uncertainty of the lead concentrations from each x-ray peak, the standard approach does not include covariance between the x-ray peaks and the coherently scattered feature. These spectral features originate from two distinct physical processes, and therefore no covariance between these features can exist. Through experimental and simulated data, we confirm that there is no observed covariance between the detected Pb x-ray peaks and the coherently scattered photon signal, as expected. This is in direct contrast to recent work published by Brito (2006 Phys. Med. Biol. 51 6125-39). There is, however, covariance introduced in the calculation of the weighted mean lead concentration due to the common coherent normalization. This must be accounted for in calculating the uncertainty of the weighted mean lead concentration, as is currently the case. We propose here an alternative approach to calculating the weighted mean lead concentration in such a way as to eliminate the covariance introduced by the common coherent normalization. It should be emphasized that this alternative approach will only apply in situations in which the calibration line intercept is not included in the calculation of the Pb concentration from the spectral data: when the source of the intercept is well characterized and known to come from trace contamination by Pb in the plaster of Paris calibration standards. In our approach, the coherent normalization is only applied to one parameter and we no longer take a weighted mean of correlated quantities. Our proposed alternative calculation has essentially no effect on the calculated error of the mean lead concentration, indicating that the existing method of accounting for this covariance is sufficient.
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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 | 0.012 | 0.026 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.003 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| 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 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".