A Bayesian approach to two-sided quickest change detection
Bibliographic record
Abstract
The problem of detecting an abrupt change in a sequence of independent and identically distributed (IID) random variables is addressed. Sequentially received samples are IID both before and after a single unknown change time. Unlike previous approaches to change detection that assume a known probability density function (PDF) for the observations at the start, the problem formulated here is to detect a change between two given PDFs in either direction, meaning that at any given time the number of hypotheses to be tracked is always twice the number of samples received. A Bayesian multiple hypothesis approach is proposed and shown to have the following properties: (i) unlike previous tests that operate with a threshold, the minimum-cost hypothesis is tracked through time, including that of no change. (ii) under an exponential delay cost function and suitable parameter choices, the proposed procedure's probability of detecting a change in the incorrect direction asymptotically vanishes with time, (iii) the method is recursive with constant computation per unit time, and (iv) error probabilities may be directly traded off with average delay. Performance results using simulation confirm the derived properties and also reveal that the additional average delay after a transient period corresponding to when the starting state is uncertain, compared to that of the optimal one-sided test, CUSUM, is modest.
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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 | 0.005 | 0.022 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".