Bayesian inference of a queueing system with short- or long-tailed distributions based on Hamiltonian Monte Carlo
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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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 | 0.005 | 0.024 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 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".