Post‐selection point and interval estimation of signal sizes in Gaussian samples
Bibliographic record
Abstract
Abstract We tackle the problem of the estimation of a vector of underlying means (signal sizes) from a single vector‐valued observationy. Often one is interested in estimating only a subvector of signals corresponding to a set of selected, “interesting” sample elements. These “interesting” sample elements tend to have the largest absolute size, gleaned by applying some selection procedure like that of Benjamini & Hochberg (2015). Previous work on this estimation task proposes the reduction in size of the largest (absolute) sample elements either via shrinkage (like James–Stein) or by subtracting biases estimated using empirical Bayes methodology. We take a novel approach and adapt recent developments by Lee et al. (2016) in post‐selection inference. Adapting and applying their distributional results to our problem post‐selection point and interval estimators for underlying signal sizes are proposed. Simulations suggest that our estimator seems to perform quite well against competitors. Furthermore we prove an upper bound to the so‐called “worst case risk” of our estimator—when combined with the Benjamini–Hochberg selection procedure—and show that it is within a constant multiple of the minimax risk over a rich set of parameter spaces meant to evoke sparsity.The Canadian Journal of Statistics45: 128–148; 2017 © 2017 Statistical Society of Canada
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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 | 0.026 | 0.125 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 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".