Overcoming the Circular Problem for Gamma‐Ray Bursts in Cosmological Global‐Fitting Analysis
Bibliographic record
Abstract
Due to the lack of low-redshift long gamma-ray bursts (GRBs), the circular problem has been a severe obstacle for using GRBs as cosmological candles. In this paper, we present a new method to deal with such a problem in Markov chain Monte Carlo (MCMC) global fitting analysis. Assuming a certain type of correlation, for the parameters involved in the correlation relation, we treat them as free parameters and determine them simultaneously with cosmological parameters through MCMC analysis on GRB data together with other observational data. Then the circular problem is naturally eliminated in this procedure. To demonstrate the feasibility of our method, we take the Ghirlanda relation ( E γ ∝ C E A peak ) as an example, while keeping in mind the debate about its physical validity. Together with SN Ia, WMAP , and SDSS data, we include 27 GRBs with the reported Ghirlanda relation in our study and perform MCMC global fitting. We consider the ΛCDM model and dynamical dark energy models, respectively. We also include the curvature of the universe in our analysis. In each case, in addition to the constraints on the relevant cosmological parameters, we obtain the best-fit values as well as the distributions of the correlation parameters A and C . With CMB+LSS+SNe+GRB data included in the analysis, the results on A and C for different cosmological models are in agreement well within a 1 σ range. It is also noted that the distributions of A and C are generally broader than the priors used in many studies in the literature. Our method can be readily applied to other GRB relations, which might be better physically motivated.
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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 | 0.028 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.002 |
| 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".