Constrained Statistical Inference: A Hybrid of Statistical Theory, Projective Geometry and Applied Optimization Techniques
Bibliographic record
Abstract
In many data applications, in addition to determining whether a given risk factor affects an outcome, researchers are often interested in whether the factor has an increasing or decreasing effect. For instance, a clinical trial may test which dose provides the minimum effect; a toxicology study may wish to determine the effect of increasing exposure to a harmful contaminant on human health; and an economist may wish to determine an individual's optimal preferences subject to a budget constraint. In such situations, constrained statistical inference is typically used for analysis, as estimation and hypothesis testing incorporate the parameter orderings, or restrictions, in the methodology. Such methods unite statistical theory with elements of projective geometry and optimization algorithms. In many different models, authors have demonstrated constrained techniques lead to more efficient estimates and improved power over unconstrained methods, albeit at the expense of additional computation. In this paper, we review significant advancements made in the field of constrained inference, ranging from early work on isotonic regression for several normal means to recent advances of constraints in Bayesian techniques and mixed models. To illustrate the methods, a new analysis of an environmental study on the health effects in a population of newborns is provided.
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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 | 0.023 | 0.065 |
| Meta-epidemiology (narrow) | 0.003 | 0.002 |
| Meta-epidemiology (broad) | 0.005 | 0.004 |
| Bibliometrics | 0.005 | 0.007 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.004 | 0.005 |
| Research integrity | 0.003 | 0.006 |
| Insufficient payload (model declined to judge) | 0.003 | 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".