Bibliographic record
Abstract
Probability theory is an area of mathematics that deals with the concept of likelihood. Probability theory is the mathematical foundation of statistical reasoning, and understanding how unpredictability impacts data is crucial for data scientists. Gaussian (normal) distribution is the most widely used distribution. It has two parameters which are mean and variance and easy to interpret. Also, the central limit theorem tells us that sums of independent random variables make the least number of assumptions. In addition, Poisson, Laplace, Beta, Pareto, Dirichelt, Binomial and Gamma Distributions are useful in different areas. The multivariate Gaussian is the most widely used joint probability density function. Covariance and correlation are used to measure the degree between two random variable’s X and Y. Chebyshev Inequality defines a topological space, which includes a sequence of elements, and let the sequence be called . Strong Law of Large Numbers Theorem use in large number of random variable in pairwise independent identically distributed and Renewal Theory is and example in Strong Law of Large Numbers Theorem.
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.
How this classification was reachedexpand
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 | 0.001 | 0.005 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".