General smoothing formulas for Markov-modulated Poisson observations
Bibliographic record
Abstract
In this paper, we compute general smoothing dynamics for partially observed dynamical systems generating Poisson observations. We consider two model classes, each Markov modulated Poisson processes, whose stochastic intensities depend upon the state of an unobserved Markov process. In one model class, the hidden state process is a continuously-valued Ito/spl circ/ process, which gives rise to a continuous sample-path stochastic intensity. In the other model class, the hidden state process is a continuous-time Markov chain, giving rise to a pure jump stochastic intensity. To compute filtered estimates of state process, we establish dynamics, whose solutions are unnormalized marginal probabilities; however, these dynamics include Lebesgue-Stieltjes stochastic integrals. By adapting the transformation techniques introduced by J. M. C. Clark, we compute filter dynamics which do not include these stochastic integrals. To construct smoothers, we exploit a duality between our forward and backward transformed dynamics and thereby completely avoid the technical complexities of backward evolving stochastic integral equations. The general smoother dynamics we present can readily be applied to specific smoothing algorithms, referred to in the literature as: Fixed point smoothing, fixed lag smoothing and fixed interval smoothing. It is shown that there is a clear motivation to compute smoothers via transformation techniques similar to those presented by J. M. C. Clark, that is, our smoothers are easily obtained without recourse to two sided stochastic integration. A computer simulation is included.
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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 | 0.002 | 0.012 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".