Count Data Time Series Models Based on Expectation Thinning
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Bibliographic record
Abstract
Motivated by modelling of unequally spaced count data time series, we propose the construction of a class of continuous-time first-order Markov processes based on the self-generalized expectation thinning operations. Properties of families of random variables leading to self-generalized expectation thinning operations are obtained. Characterization results are obtained for stationary marginal distributions, the innovation random variables and the infinitesimal innovation. The transition matrix and distribution of sojourn time are also derived. Particular families of self-generalized random variables are given to make the theory concrete for modelling count data that are overdispersed relative to Poisson. We also show that the self-generalizability condition is important in order to get nice properties for the Markov processes.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.002 |
| Open science | 0.002 | 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