Calibration of<sup>109</sup>Cd KXRF systems for<i>in vivo</i>bone lead measurements: weighted least-squares regression with different weighting functions
Bibliographic record
Abstract
The use of iteratively reweighted least squares (IRLS) has recently been described as an alternative to ordinary least squares with heteroscedastic data, in the calibration of (109)Cd KXRF systems for in vivo bone lead measurements. This work addresses the use of weighted least squares (WLS) with two different weighting functions and no iteration, with that same data set. The functions are defined as the inverse of the variance of observed ratios of lead to coherent peak amplitudes and the inverse of the square of the error reported by the Marquardt fitting program for these ratios. The results show that if no iteration is implemented when using WLS, then the two weighting functions are highly inefficient in homogenizing the residual variance. Moreover, both methods estimate much more imprecise calibration intercepts and slopes than did the IRLS method. Work is in progress to investigate the implementation of IRLS with these weighting functions, with the focus on the selection of the best function for residuals to be used in each iteration stage.
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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 | 0.007 | 0.024 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.003 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.002 | 0.003 |
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".