Robust<tex>$M$</tex>-ary Detection Filters and Smoothers for Continuous-Time Jump Markov Systems
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Bibliographic record
Abstract
In this paper, we consider a dynamic M-ary detection problem when Markov chains are observed through a Wiener process. These systems are fully specified by a candidate set of parameters, whose elements are, a rate matrix for the Markov chain and a parameter for the observation model. Further, we suppose these parameter sets can switch according to the state of an unobserved Markov chain and thereby produce an observation process generated by time varying (jump stochastic) parameter sets. Given such an observation process and a specified collection of models, we estimate the probabilities of each model parameter set explaining the observation. By defining a new augmented state process, then applying the method of reference probability, we compute matrix-valued dynamics, whose solutions estimate joint probabilities for all combinations of candidate model parameter sets and values taken by the indirectly observed state process. These matrix-valued dynamics satisfy a stochastic integral equation with a Wiener process integrator. Using the gauge transformation techniques introduced by Clark and a pointwise matrix product, we compute robust matrix-valued dynamics for the joint probabilities on the augmented state space. In these new dynamics, the observation Wiener process appears as a parameter matrix in a linear ordinary differential equation, rather than an integrator in a stochastic integral equation. It is shown that these robust dynamics, when discretised, enjoy a deterministic upper bound which ensures nonnegative probabilities for any observation sample path. In contrast, no such upper bounds can be computed for Taylor expansion approximations, such as the Euler-Maryauana and Milstein schemes. Finally, by exploiting a duality between causal and anticausal robust detector dynamics, we develop an algorithm to compute smoothed mode probability estimates without stochastic integrations. A computer simulation demonstrating performance is included.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 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 | 0.000 |
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