Multistate Bayesian Control Chart Over a Finite Horizon
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Bibliographic record
Abstract
We study a multistate partially observable process control model with a general state transition structure. The process is initially in control and subject to Markovian deterioration that can bring it to out-of-control states. The process may continue making transitions among the out-of-control states, or even back to the in-control state until it reaches an absorbing state. We assume that at least one out-of-control state is absorbing. The objective is to minimize the expected total cost over a finite horizon. By transforming the standard Cartesian belief space into the spherical coordinate system, we show that the optimal policy has a simple control-limit structure. We also examine two specialized models. The first is the phase-type transition time model, in which we develop an algorithm whose complexity is not affected by the number of phases. The second is a model with multiple absorbing out-of-control states, by which we show that certain out-of-control states may incur less total cost than the in-control state, a phenomenon never occurs in the two-state models. We conclude that there are fundamental differences between multistate models and two-state models, and that the spherical coordinate transformation offers significant analytical and computational benefits.
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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 | 0.005 | 0.034 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.002 |
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 it