Discrete-space particle filters for reflecting diffusions
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
We consider the low observable filtering problem of detecting and tracking a target buried in high amplitude synthetic spatial observation noise. Motivated by fish farming applications, we constrain our target to live in a rectangular region, undergoing reflections at the boundary of this region, and moving in a manner described by the unique solution to a Skorohod stochastic differential equation. Observations are taken at discrete times and consist of a nonlinear partial function of the current state corrupted by additive noise. We use the reference probability method to describe the solution to this filtering problem in terms of a discrete-time version of the Duncan-Mortensen-Zakai equation and then use Markov chain approximations to produce an implementable approximate solution. The approximations incorporate discretizations of both space and amplitude directly into the unnormalized conditional distribution of the signal given the back observations. These approximations converge to the actual filtering conditional distribution as the discretization mesh is refined. The algorithm to implement our filter is reduced to an algorithm to implement a specific time-inhomogeneous Markov chain, which can be done using a single Poisson process and independent sequences of Bernoulli trials. The inhomogeneity is due to the observations themselves. The discretization of amplitude results in particles representing a small mass of the conditional distribution at particular grid points in the signal domain. These particles diffuse, drift, give birth, and die within the region similarly to those of continuous-state particle filters. The particles include information from the observations through observation-dependent births and deaths. We discuss issues like mean time to localize the target and fidelity of filter estimates at various signal to noise ratios, and give visual demonstrations of filter performance.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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) | 0.000 | 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