Tolerance bands for exponential family functional data
Bibliographic record
Abstract
Abstract A tolerance band for a functional response provides a region that is expected to contain a given fraction of observations from the sampled population at each point in the domain. This band is a functional analogue of the tolerance interval for a univariate response. Although the problem of constructing functional tolerance bands has been considered for a Gaussian response, it has not been investigated for non‐Gaussian responses, which are common in biomedical applications. We describe a methodology for constructing tolerance bands for two non‐Gaussian members of the exponential family: binomial and Poisson. The approach is to first model the data using the framework of generalized functional principal components analysis. Then, a parameter is identified in which the marginal distribution of the response is stochastically monotone. We show that the tolerance limits can be readily obtained from confidence limits for this parameter, which in turn can be computed using large‐sample theory and bootstrapping. Our proposed methodology works for both dense and sparse functional data. We report the results of simulation studies designed to evaluate its performance and get recommendations for practical applications. We illustrate our proposed method using two actual biomedical studies, and also provide computer source code that implements our method.
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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 | 0.037 | 0.165 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.004 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 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".