On uncertainty estimation in functional linear mixed models
Bibliographic record
Abstract
Abstract Functional data analysis has proven useful in many scientific applications where a physical process is observed as a curve. In many applications, several curves are observed due to multiple subjects, providing replicates in the statistical sense. Recent literature develops several techniques for registering curves and estimating associated models in a regression framework. Standard regression models ignore heterogeneity among curves. Functional linear mixed models are one popular way to combine several curves and capture variability among curves via random effects. Although there is a good amount of work available for analyzing functional data using mixed models, limited attention has been paid to inference. After estimation, we concentrate on measuring uncertainty in terms of mean squared error when functional linear mixed models are used for prediction. Although measuring uncertainty is of paramount interest in any statistical prediction, there is no theoretically valid expression available for functional mixed effect models. The quality of theoretical approximations depends on the number of curves observed. In many real life applications, only a finite number of curves can be observed. In such situations, it is important to asses the error rate for any valid statistical statement. In this article, we derive a theoretically valid approximation of uncertainty measurements for prediction. We also provide some modifications for model estimation. The empirical performance of the proposed method is investigated by numerical examples and is compared with existing literature as appropriate. Our method is computationally simple and often outperforms other existing methods.
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How this classification was reachedexpand
Direct model labels (unvalidated)
Per-model category and study-design labels from the labeling rounds. They are machine output, unvalidated, and the disagreement between models ships as data. No study design here is MEDLINE-validated yet.
| Model arm | Categories | Study design | Confidence |
|---|---|---|---|
| gpt | no category Domain: not available · Genre: Methods About the Canadian research system: no · About a Canadian topic: no | Simulation or modeling | high |
| grok | no category Domain: not available · Genre: Methods About the Canadian research system: no · About a Canadian topic: no | Simulation or modeling | high |
| opus | no category Domain: not available · Genre: Methods About the Canadian research system: no · About a Canadian topic: no | Simulation or modeling | high |
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 | 0.000 | 0.009 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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 itClassification
machine, unvalidatedLabeled directly by 3 models reading the full record.
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".