Cosmological measurements from the CMB and BAO are insensitive to the tail probability in the assumed likelihood
Bibliographic record
Abstract
Abstract When fitting cosmological models to data, a Bayesian framework is commonly used, requiring assumptions on the form of the likelihood and model prior. In light of current tensions between different data, it is interesting to investigate the robustness of cosmological measurements to statistical assumptions about the likelihood distribution from which the data was drawn. We consider the impact of changes to the likelihood caused by uncertainties due to the finite number of mock catalogs used to estimate the covariance matrix, leading to the replacement of the standard Gaussian likelihood with a multivariate t-distribution. These changes to the likelihood have a negligible impact on recent cosmic microwave background (CMB) lensing and baryon acoustic oscillation (BAO) measurements, for which covariance matrices were measured from mock catalogs. We then extend our analysis to perform a sensitivity test on the Gaussian likelihoods typically adopted, considering how increasing the size of the tails of the likelihood (again using a t-distribution) affects cosmological inferences. For an open ΛCDM model constrained by BAO alone, we find that increasing the weight in the tails shifts and broadens the resulting posterior on the parameters, with a ∼0.2–0.4σ effect on ΩΛ and Ωk. In contrast, the CMB temperature and polarization constraints in ΛCDM showed less than 0.03σ changes in the parameters, except for {τ, ln(1010 A s), σ 8, S 8, σ 8Ω0.25 m, z re, 109 A s e -2τ } which shifted by around 0.1–0.2σ. If we use solely ℓ < 30 data, the amplitude A s e -2τ varies in the posterior mean by 0.7σ and the error bars increase by 6%. We conclude, at least for current-generation CMB and BAO measurements, that uncertainties in the shape and tails of the likelihood do not contribute to current tensions.
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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 | 0.011 | 0.102 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".