Hierarchical Bayes Analysis of Rare Events Using High-Dispersion Poisson Mixtures
Why this work is in the frame
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Bibliographic record
Abstract
Modeling the occurrence of rare events such as multiyear ice or iceberg encounters, ship collisions, and several types of accidental events is often challenging because considerable dispersion is found to be associated with discrete count data. This may be due to fluctuations in the processes generating the events, or they may arise because of a complicated mixture of causal events or there may be other unexplained discontinuities. In such cases, the traditional use of the Poisson distribution is inadequate, especially when the event frequency is subsequently used to formulate design criteria based on extreme values. In this paper, the use of discrete Poisson mixtures is suggested as opposed to the simple Poisson process and continuous Poisson mixtures. One objective is to ensure that the uncertainty regarding event occurrence is well represented in both the central and tail parts of count data. The analysis of discrete Poisson mixtures involves the estimation of the number k of mixture components, the k Poisson occurrence rates, and the k weights of the mixture. Until recently such an analysis was considered daunting at best. However, the analysis can be re-cast as an equivalent Hierarchical Bayes (HB) net using an auxiliary variable vector Z of variable dimension. A Markov Chain Monte Carlo analysis can then be used to obtain the posterior distributions of the dimensionality of the mixture, the mixture weights and the occurrence rates themselves. Also, posterior distributions can be found for iceberg collision risks and iceberg scour rates. The approach is illustrated for an iceberg risk estimation.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| 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) | 0.001 | 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