Inequalities between expected marginal log‐likelihoods, with implications for likelihood‐based model complexity and comparison measures
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Abstract A multi‐level model allows the possibility of marginalization across levels in different ways, yielding more than one possible marginal likelihood. Since log‐likelihoods are often used in classical model comparison, the question to ask is which likelihood should be chosen for a given model. The authors employ a Bayesian framework to shed some light on qualitative comparison of the likelihoods associated with a given model. They connect these results to related issues of the effective number of parameters, penalty function, and consistent definition of a likelihood‐based model choice criterion. In particular, with a two‐stage model they show that, very generally, regardless of hyperprior specification or how much data is collected or what the realized values are, a priori, the first‐stage likelihood is expected to be smaller than the marginal likelihood. A posteriori, these expectations are reversed and the disparities worsen with increasing sample size and with increasing number of model levels.
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.
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it