A convenient approach to characterizing model uncertainty with application to early dark energy solutions of the Hubble tension
Bibliographic record
Abstract
ABSTRACT Despite increasingly precise observations and sophisticated theoretical models, the discrepancy between measurements of H0 from the cosmic microwave background or from baryon acoustic oscillations combined with big bang nucleosynthesis versus those from local distance ladder probes – commonly known as the ‘H0 tension’ – continues to perplex the scientific community. To address this tension, early dark energy (EDE) models have been proposed as alternatives to Lambda cold dark matter, as they can change the observed sound horizon and the inferred Hubble constant from measurements based on this. In this paper, we investigate the use of Bayesian model averaging (BMA) to evaluate EDE as a solution to the H0 tension. BMA consists of assigning a prior to the model and deriving a posterior as for any other unknown parameter in a Bayesian analysis. BMA can be computationally challenging in that one must approximate the joint posterior of both model and parameters. Here, we present a computational strategy for BMA that exploits existing Markov chain Monte Carlo software and combines model-specific posteriors post hoc. In application to a comprehensive analysis of cosmological data sets, we quantify the impact of EDE on the H0 discrepancy. We find an EDE model probability of ${\sim} 90~{{\ \rm per\ cent}}$ whenever we include the H0 measurement from Type Ia supernovae in the analysis, whereas the other data show a strong preference for the standard cosmological model. We finally present constraints on common parameters marginalized over both cosmological models. For reasonable priors on models with and without EDE, the H0 tension is reduced by at least 20 per cent.
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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 | 0.012 | 0.063 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| 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".