Optimal Design for Estimation in Diffusion Processes from First Hitting Times
Bibliographic record
Abstract
We consider the optimal design problem for the Ornstein--Uhlenbeck process with fixed threshold, commonly used to describe a leaky, noisy integrate-and-fire neuron. We present a solution to the problem of devising the best external time-dependent perturbation to the process in order to facilitate the estimation of the characteristic time parameter for this process. The optimal design problem is constrained here by the fact that only the times between threshold crossings from below, known as hitting times, are observable. The optimal control is based on a maximization of the mutual information between the posterior of the unknown parameter given these observations and the distribution of the hitting times. Our approach is based on the adjoint method for computing the gradient of a functional of a solution to a Fokker--Planck partial differential equation with respect to an input function (i.e., to the control). Our method also enables the estimation of other parameters, in the case when more than one parameter is unknown.
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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 | 0.007 | 0.018 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| 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".