Bibliographic record
Abstract
Abstract We discuss inference for graphical models as a multiple comparison problem. We argue that posterior inference under a suitable hierarchical model can adjust for the multiplicity problem that arises by deciding inclusion for each of many possible edges. We show that inference under that hierarchical model differs substantially from inference under a comparable non‐hierarchical model. With increasing size of the graph the difference between posterior distributions under the two models, as measured by Kullback–Liebler (KL) divergence, increases. We discuss several stylized inference problems, including estimation of one graph, comparison of a pair of graphs, estimation of a pair of graphs and, finally, estimation for multiple graphs. Throughout the discussion we assume that the graph is used to identify a conditional independence structure, that is, the graph represents a Markov random field. Model construction starts with a prior model for the random graph, conditional on which a sampling model is proposed for the observed data. There are no constraints on the nature of the sampling model. Most of the discussion is general and remains valid for any sampling model, subject to some technical constraints only. The discussion is motivated by two case studies. The first application is to model single cell mass spectrometry data for inference about the joint distribution of a set of markers that are recorded for each cell. Another application is to model Reverse Phase Protein Arrays (RPPA) protein expression data, for inference about changes of underlying biomolecular pathways across three biologic conditions of interest.The Canadian Journal of Statistics45: 44–61; 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 | 0.064 | 0.247 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.004 | 0.003 |
| Bibliometrics | 0.004 | 0.004 |
| Science and technology studies | 0.002 | 0.009 |
| Scholarly communication | 0.005 | 0.010 |
| Open science | 0.008 | 0.006 |
| Research integrity | 0.004 | 0.007 |
| Insufficient payload (model declined to judge) | 0.012 | 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".