Computation of normalizing constants in geoacoustic Bayesian inference.
Bibliographic record
Abstract
This paper considers approaches to computing normalizing constants (Z) in Bayesian inference problems. Bayes’ theorem combines the likelihood function, model prior, and Z to form the posterior probability density (PPD). Z (also known as evidence) is difficult to compute for general problems and a common approach is to avoid its computation entirely by calculating an unnormalized estimate of the PPD which is sufficient for moment estimates. However, estimating the normalized PPD, including Z, allows for moment estimates as well as quantifying the likelihood of the model parametrization. This is commonly referred to as model selection and poses a natural way to quantifying the most appropriate model parametrization for a given data set (Bayesian razor). Several approaches for computing Z have been developed in the statistics community, some of which are applied here to the geoacoustic inference problem. Annealed importance sampling follows an annealing approach and computes weighted averages along cooling trajectories. Nested sampling uses a likelihood constraint to move from the prior mass to the posterior. Both methods also give parameter estimates which are compared to Metropolis–Hastings results. [Work supported by the Office of Naval Research.]
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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 | 0.016 | 0.097 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.004 | 0.004 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.004 | 0.008 |
| Open science | 0.005 | 0.005 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.006 | 0.002 |
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".