Bibliographic record
Abstract
We demonstrate that the processes underlying on-line auction price bids and many\n other longitudinal data can be represented by an empirical first order stochastic ordinary\n differential equation with time-varying coefficients and a smooth drift process. This\n equation may be empirically obtained from longitudinal observations for a sample of\n subjects and does not presuppose specific knowledge of the underlying processes. For the\n nonparametric estimation of the components of the differential equation, it suffices to\n have available sparsely observed longitudinal measurements which may be noisy and are\n generated by underlying smooth random trajectories for each subject or experimental unit in\n the sample. The drift process that drives the equation determines how closely individual\n process trajectories follow a deterministic approximation of the differential equation. We\n provide estimates for trajectories and especially the variance function of the drift\n process. At each fixed time point, the proposed empirical dynamic model implies a\n decomposition of the derivative of the process underlying the longitudinal data into a\n component explained by a linear component determined by a varying coefficient function\n dynamic equation and an orthogonal complement that corresponds to the drift process. An\n enhanced perturbation result enables us to obtain improved asymptotic convergence rates for\n eigenfunction derivative estimation and consistency for the varying coefficient function\n and the components of the drift process. We illustrate the differential equation with an\n application to the dynamics of on-line auction data.
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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 | 0.008 | 0.040 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".