Two-sided change detection under unknown initial state
Bibliographic record
Abstract
The problem of detecting a change in distribution of a sequence of independent and identically distributed (IID) random variables is addressed. Unlike previous approaches to sequential change detection, which assume a known initial probability density function (PDF) for the sequence, in this paper we address the case where the initial distribution of the sequence is unknown. An optimal stopping approach based on Bayesian hypothesis testing with exponential delay cost is proposed. The tradeoffs among average detection delay, probability of false alarm and probability of detecting a change in the incorrect direction are investigated. It is shown that the proposed test's probability of change detection in the incorrect direction can be made arbitrarily small without significantly increasing average detection delay for change times larger than a minimum value determined by the hypothesis testing problem itself. The proposed test also has a recursive algorithm to track the minimum risk hypotheses with fixed complexity per sample. Simulation results confirm the derived properties and reveal that the average delay, after an initial transient period, approaches that of the CUSUM test, which is delay-optimal if the initial state were known.
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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 | 0.003 | 0.024 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".