On deriving Liouville process from Liouville distribution and its application in nonparametric Bayesian inference
Bibliographic record
Abstract
The Liouville distribution, a generalization of the Dirichlet distribution, serves as a well-known conjugate prior for the multinomial distribution. Just as the Dirichlet process is derived from the finite-dimensional Dirichlet distribution, it is natural and important to introduce and derive a Liouville process in a similar manner. We introduce a discrete random probability measure constructed from a random vector following a Liouville distribution and subsequently derive its weak limit to define our proposed Liouville process. The resulting process is a spike-and-slab process, where the Dirichlet process serves as the slab and a single point from its mean acts as the spike. These two components are linearly combined using a random weight generated from the Liouville distribution. By using the Liouville process as a prior on the space of probability measures, we derive the corresponding posterior process as well as the predictive distribution.
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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 | 0.008 | 0.030 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.003 | 0.004 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.003 | 0.005 |
| 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".