On the numerical stability of time-discretised state estimation via clark transformations
Bibliographic record
Abstract
In this article we consider the numerical stability of discretisation schemes for continuous time state estimation filters. The dynamical systems we consider model the indirect observation of a continuous time Markov chain. Two candidate observation models are studied. These models are, a) the observation of a state process through a Brownian motion, and b) the observation of a state process through a Poisson process. For the models just described, one can choose between several different approximate discrete time recursions. However, most of these schemes suffer an inherent instability, that is, their estimated filter probabilities can be negative (with a nonzero probability). We show that there is an exception to this problem, afforded by the so called robust filters due to J. M. C. Clark. It is shown that for the said robust filter, one can ensure nonnegative estimated probabilities by choosing a maximum grid step to be no greater than a given bound. The importance of this result, is one can choose a priori, a grid step maximum ensuring nonnegative estimated probabilities. In contrast, no such upper bound is available for the standard approximation schemes. Further, this upper bound also applies to the corresponding robust smoothing scheme, in turn ensuring stability for smoothed state estimates.
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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 | 0.004 | 0.022 |
| 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 | 0.003 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| 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".