A comprehensive approach to analyzing environmental data with non-detects
Bibliographic record
Abstract
Non-detects—measurements reported as “below the detection limit”—are ubiquitous in environmental science and engineering. They are frequently replaced with a constant, but this biases estimates of means, regression slopes, and correlation coefficients. Omitting non-detects is worse, and has led to serious errors. Simple alternatives are available: rank-based statistics, maximum likelihood estimation, and re-purposed survival analysis routines. But many environmental datasets do not align well with the assumptions these methods make—it is often necessary to account for hierarchy (e.g., measurements nested within lakes), sampling strategy (e.g., measurements collected as time series), heterogeneity (e.g., site-dependent variance), and measurement error. Bayesian methods offer the flexibility to do this; incorporating non-detects is also easy and does not bias model parameter estimates as substitution does. Here we discuss Bayesian implementations of common bivariate and multivariate statistical methods relevant to environmental science. We use a dataset comprising time series of Ag, As, Cd, Ce, Co, Sb, Ti, U, and V concentrations in municipal biosolids that includes many non-detects. The models can be reproduced and extended to new problems using the data and code accompanying this paper.
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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 | 0.018 | 0.046 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.002 | 0.004 |
| Bibliometrics | 0.005 | 0.008 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.006 | 0.005 |
| Open science | 0.004 | 0.005 |
| Research integrity | 0.003 | 0.006 |
| Insufficient payload (model declined to judge) | 0.004 | 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".