Poisson Mean Homogeneity: Single-Observation Framework with Applications
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
Practical problems often drive the development of new statistical methods by presenting real-world challenges. Testing the homogeneity of n independent Poisson means when only one observation per population is available is considered in this paper. This scenario is common in fields where limited data from multiple sources must be analyzed to determine whether different groups share the same underlying event rate or mean. These settings often exhibit underlying structural or spatial symmetries that influence statistical behavior. Traditional methods that rely on large sample sizes are not applicable. Hence, it is crucial to develop techniques tailored to the constraints of single observations. Under the null hypothesis, with large n and a fixed common mean λ, the likelihood ratio test statistic (LRTS) is shown to be asymptotically normally distributed, with the mean and variance being approximated by a truncation method and a parametric bootstrap method. Moreover, with fixed n and large λ, under the null hypothesis, the LRTS is shown to be asymptotically distributed as a chi-square with n−1 degrees of freedom. The Bartlett correction method is applied to improve the accuracy of the asymptotic distribution of the LRTS. We highlight the practical relevance of the proposed method through applications to wildfire and radioactive event data, where correlated observations and sparse sampling are common. Simulation studies further demonstrate the accuracy and robustness of the test under various scenarios, making it well-suited for modern applications in environmental science and risk assessment.
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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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