Observability and Filter Stability for Partially Observed Markov Processes
Why this work is in the frame
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Bibliographic record
Abstract
Filter stability is a classical problem for partially observed Markov processes (POMP). For a POMP, an in-correctly initialized non-linear filter is said to be stable if the filter eventually corrects itself with the arrival of new measurement information. In this paper, we first introduce a functional characterization of observability for a POMP and show that this characterization is sufficient to guarantee stability of the non-linear filter in a weak sense. Under further regularity conditions, we establish stability under the notions of weak convergence, total variation, and relative entropy; thus complementing and also unifying some existing results in the literature. In addition, we study controlled partially observed Markov decision processes (POMDP) to arrive at analogous stability once control, and hence non-Markovian dependence between random variables, is introduced into the system. This brings together results in non-linear filtering theory and stochastic control theory which had previously remained isolated.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it