The Pie sharing problem: Unbiased sampling of N+1 summative weights.
Bibliographic record
Abstract
The Pie sharing problem: Unbiased sampling of N+1 summative weights. by J. Mai 1, J. R. Craig 1, and B. A. Tolson 1 1 Dept. Civil and Environmental Engineering, University of Waterloo, Waterloo, ON, Canada. Abstract A simple algorithm is provided for randomly sampling a set of N+1 weights such that their sum is constrained to be equal to one, analogous to randomly subdividing a pie into N+1 slices where the probability distribution of slice volumes are identically distributed. The cumulative density and probability density functions of the random weights are provided. The algorithmic implementation for the random number sampling are made available. This algorithm has potential applications in calibration, uncertainty analysis, and sensitivity analysis of environmental models. The associated journal publication provides three example applications to demonstrate the efficiency and superiority of the proposed method compared to alternative sampling methods. Please refer to the Wiki for more details and documentation. Usage Please refer to the Wiki for details on the usage in Python and R. Citation Journal publication J. Mai, J. R. Craig, and B. A. Tolson (2021). The Pie sharing problem: Unbiased sampling of N+1 summative weights. Environmental Modelling and Software. Under review. Code publication J. Mai, J. R. Craig, and B. A. Tolson (2020). The PieShareDistribution: Unbiased sampling of N+1 summative weights. Zenodo. https://doi.org/10.5281/zenodo.4300332 Release information This is the first release of the PieShareDistribution which is sampling N random numbers that add up to 1.0 while all the N random variables are independently and identically distributed (i.i.d.). This might become in handy when you for example want to sample soil textures (soil, sand, clay percentage) making sure that the soil triangle is sampled uniformly.
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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 | 0.014 | 0.047 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.013 | 0.003 |
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".