A statistical test for mixture detection with application to component identification in multidimensional biomolecular NMR studies
Bibliographic record
Abstract
Abstract We introduce a statistical hypothesis test for detecting mixtures in a nonlinear regression model with mean regression function defined by a weighted sum of two multidimensional unimodal functions, where each unimodal function in the summation representing acomponent. Two regression components are mixed when the distance between their centres is small or the proportion of their contribution to the mean regression function is close to zero or one. Two challenges in model estimation under the null hypothesis of one regression component are that the proportion parameter describing the weighed contribution of each component lies on the boundary of the parameter space and that the model parameters are nonidentifiable. Therefore, the parameter estimators derived from standard nonlinear estimation approaches are inconsistent and unstable. To overcome these challenges, we study a penalized regression test statistic with a relatively simple quadratic approximation which can be used to simulate the quantiles of the test statistic under the null hypothesis. One leading application of the mixture testing procedure is the detection of mixed or overlapped components in multidimensional data generated from nuclear magnetic resonance (NMR) experiments for protein structure determination. It is important to de‐mix the components since each regression component provides specific information about the structure of the protein. In certain cases, the lack of a small number of essential components can lead to a significant deviation in the predicted structure.The Canadian Journal of Statistics42: 36–60; 2014 © 2013 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 | 0.065 | 0.289 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.004 | 0.003 |
| Bibliometrics | 0.006 | 0.005 |
| Science and technology studies | 0.002 | 0.008 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.006 | 0.004 |
| Research integrity | 0.005 | 0.005 |
| Insufficient payload (model declined to judge) | 0.005 | 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".