A gentle introduction to the Poisson process assumptions in a probability course
Bibliographic record
Abstract
A first glance by probability students at the assumptions underlying the Poisson process can lead to confusion and possibly anxiety. Although attempts are usually made to describe the assumptions in words, the motivation behind the assumptions is often unclear, and the eventual derivation of the Poisson distribution formulae can then appear to be quite magical. In fact, it is a beautiful result, and the Bernoulli process provides a way for more students to be able to appreciate all aspects of a Poisson process model and its derivation. A small number of authors have been using the Bernoulli process as an approximation to the Poisson process; the present paper adopts their approach and outlines a teaching strategy that leads from the more naturally defined Bernoulli process assumptions to the Poisson process assumptions.
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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 | 0.004 | 0.014 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.003 | 0.011 |
| Insufficient payload (model declined to judge) | 0.037 | 0.026 |
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".