Observability and Filter Stability for Partially Observed Markov Processes
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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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 | 0.012 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".