Bibliographic record
Abstract
The essentials of probability and random processes required in the text are outlined. In this chapter as well as in succeeding chapters, numerical results illustrate the theoretical results. These results are obtained using three different tools as appropriate to the work at hand: Excel, Matlab and Maple. Starting with set theory, and the axioms of probability we derive basic relations, and the concepts of conditional probabilities and independence. The next section deals with random variables and their distribution and density functions. The discussion is in two parts dealing with discrete and continuous random variables, respectively and covers all of the widely used random variables. The probability generating function for discrete random variables and the Laplace transform for continuous random variables receive particular attention because of their role in the text. In subsequent sections, the discussion of basic probability theory is completed with discussions of joint random variables, transformations of random variables and bounds on probabilistic events. The final half of the chapter deals with the fundamentals of Markov chains and of random processes.
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 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 | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.004 | 0.005 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.004 | 0.006 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.020 | 0.013 |
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".