Maximum entropy estimation of the probability density function from the histogram using order statistic constraints
Why this work is in the frame
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Bibliographic record
Abstract
An analytical expression for a probability density is usually required in detection and estimation problems, yet it is usually only assumed or selected from contenders by parameter estimation, or the histogram is smoothed with an arbitrary window function. In contrast, given a histogram containing R sample points, we derive a nonlinear differential equation (NDEQ) whose solution is a maximum entropy density given constraints that arise from assumptions that the samples are means of the order statistics of the parent distribution. We solve the NDEQ for R=1 and approximate the solution for general R using the fact that order means partition the density into equal probability regions, which we require to independently be maximum entropy. Finally we show with a Rayleigh density example what errors may result.
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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 | 0.000 | 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 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.005 | 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