Three-parameter stochastic lognormal diffusion model: statistical computation and simulating annealing – application to real case
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
In this paper, we propose a new study of a stochastic lognormal diffusion process (SLDP), with three parameters, which can be considered as an extension of the bi-parametric lognormal process with the addition of a threshold parameter. From the Kolmogorov equation, we obtain the probability density function and the moments of this process. The statistical inference of the parameter is studied by considering discrete sampling of the sample paths of the model and then using the maximum likelihood (ML) method. The estimation of the threshold parameter requires the solution of a nonlinear equation. To do so, we propose two methods: the classical Newton–Raphson (NR) method and one based on simulated annealing (SA). This methodology is applied to an example with simulated data corresponding to the process with known parameters. From this, we obtain the estimators of the parameters by both methods (NR and SA). Finally, the methodology studied is applied to a real case concerning the mean age of males in Spain at the date of their first wedding.
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 | 0.001 |
| 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