Bayesian inference of a queueing system with short- or long-tailed distributions based on Hamiltonian Monte Carlo
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Bibliographic record
Abstract
In this paper, we deal with a Bayesian inference method for estimating the parameters of the queueing system with short- or long-tailed distributions based on the No-U-Turn Sampler (NUTS), a recently developed Hamilton Monte Carlo (HMC). We assume inter-arrival and service times to be either the short-tailed distributions or the long-tailed distributions since they are a better fit for real-world data. We illustrate our assumption using a number of simulated data sets, generated from distributions covering a wide range of cases. Then we estimate the parameters using the Bayesian approach based on No-U-Turn Sampler. As a result of comparing the No-U-Turn Sampler with the Gibbs sampler, the most common MCMC algorithm, we demonstrate that the NUTS outperforms Gibbs sampler for estimating parameters, which is especially significant for long-tailed distribution. We also investigate the influence of the size of observation data and the prior distributions on estimating these parameters.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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