Bibliographic record
Abstract
The univariate noncentral distributions can be derived by multiplying their central distributions with translation factors. When constructed in terms of translated uniform distributions on unit radius hyperspheres, these translation factors become generating functions for classical families of orthogonal polynomials. The ultraspherical noncentral t, normal N, F, and χ2 distributions are thus found to be associated with the Gegenbauer, Hermite, Jacobi, and Laguerre polynomial families, respectively, with the corresponding central distributions standing for the polynomial family-defining weights. Obtained through an unconstrained minimization of the Gibbs potential, Jaynes’ maximal entropy priors are formally expressed in terms of the empirical densities’ entropic convex duals. Expanding these duals on orthogonal polynomial bases allows for the expedient determination of the Jaynes–Gibbs priors. Invoking the moment problem and the duality principle, modelization can be reduced to the direct determination of the prior moments in parametric space in terms of the Bayes factor’s orthogonal polynomial expansion coefficients in random variable space. Genomics and geophysics examples are provided.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.003 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| 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".