Multiple change‐point models for time series
Bibliographic record
Abstract
Abstract The “Bayes‐type” method of deriving change‐point test statistics was introduced by Chernoff and Zacks (1964). Other authors subsequently adapted this approach and derived Bayes‐type statistics for at most one change (AMOC), and for multiple change points, under a variety of model formulations. Asymptotic distribution theory has always been limited to the AMOC statistics because of the perceived complexity of multiple change‐point statistics. In this article, it is shown that the Bayes‐type statistic derived to test for multiple change points is directly proportional to the AMOC statistic. This result immediately provides distributional results for Bayes‐type multiple change‐point statistics. In addition, it fundamentally alters the current understanding of the AMOC statistic. It follows from this result that the Bayes‐type statistic derived under AMOC conditions in fact tests for at least one change (ALOC), even though the statistic is derived under AMOC formulation. Under asymptotic consideration, the result also extends to the case of model errors following a stationary process. As an example, the classical Nile River data are revisited and analyzed for the presence of multiple change points.
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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 | 0.022 | 0.068 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.004 | 0.003 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.004 | 0.002 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 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".