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Applying the BF method on the DESI evidence for dynamical dark energy models

Ziad Sakr

TL;DR

The paper addresses the robustness of Bayesian model comparison between a dynamical dark-energy CPL model and a $w$CDM baseline in the DESI era, noting strong prior sensitivity in Bayes factor conclusions. It introduces a Bayesian-Frequentist (FB) hybrid approach that treats the Bayes factor $B = E_A/E_B$ as a random variable and samples its distribution by perturbing data, with $E(D|M) = \int L(D|\theta,M) P(\theta|M) d\theta$ and $\beta = 2\ln B$ decomposed into the distance between fits, the Occam penalty $Y_M = \ln|F_M|/|P_M|$, and prior-to-posterior gains. The results show fixed-$B$ conclusions are highly prior-dependent, while the BF method yields CPL over $w$ as the preferred trend across priors but with reduced significance, and covariance perturbations further dampen discriminating power. The approach provides a robust framework for model comparison in cosmology and should be employed for future DESI data to mitigate spurious claims of dynamical dark energy.

Abstract

Recent baryon acoustic oscillation measurements from the DESI, when combined with CMB data and Type Ia supernovae observations, indicate a preference for dynamical dark energy when considering the Chevallier-Polarski-Linder (CPL) model, over the standard ΛCDM or the wCDM model. However, the Bayes factor, a key metric for model comparison, remains inconclusive on which model is preferred. This paper applies the BF method, that integrates both Bayesian and frequentist approaches to DESI data to address the limitations of purely frequentist or Bayesian methods. It consists in considering the Bayes factor as a random variable and calculates its distribution, that results from values computed in a frequentist approach after perturbing the data following the model considered. We apply this hybrid method to DESI data, comparing the CPL and w models under various prior conditions, including weak and strong priors, and theory-informed priors. We find that, when the traditional bayes factor is considered, that weak priors favor the w model over CPL, while strong priors favor CPL. Additionally, theory-informed priors further enhance the preference for the w model. While when we apply the BF method, the preference for CPL over w is seen in all cases albeit with similar but reduced impact on the p-value from the different prior considerations. We also tried to generalize further, by perturbing as well the covariance matrix following the model considered, and found that, in general, the current data in that case is not stringent enough to disentangle between the two models. Our results demonstrate that varying the Bayes factor as a random variable, providing that the covariance matrix is kept as model independent, provides a robust model comparison, reducing the impact of prior dependence as well as offering quantitative assessment of the preferences of the competing models.(abridged)

Applying the BF method on the DESI evidence for dynamical dark energy models

TL;DR

The paper addresses the robustness of Bayesian model comparison between a dynamical dark-energy CPL model and a CDM baseline in the DESI era, noting strong prior sensitivity in Bayes factor conclusions. It introduces a Bayesian-Frequentist (FB) hybrid approach that treats the Bayes factor as a random variable and samples its distribution by perturbing data, with and decomposed into the distance between fits, the Occam penalty , and prior-to-posterior gains. The results show fixed- conclusions are highly prior-dependent, while the BF method yields CPL over as the preferred trend across priors but with reduced significance, and covariance perturbations further dampen discriminating power. The approach provides a robust framework for model comparison in cosmology and should be employed for future DESI data to mitigate spurious claims of dynamical dark energy.

Abstract

Recent baryon acoustic oscillation measurements from the DESI, when combined with CMB data and Type Ia supernovae observations, indicate a preference for dynamical dark energy when considering the Chevallier-Polarski-Linder (CPL) model, over the standard ΛCDM or the wCDM model. However, the Bayes factor, a key metric for model comparison, remains inconclusive on which model is preferred. This paper applies the BF method, that integrates both Bayesian and frequentist approaches to DESI data to address the limitations of purely frequentist or Bayesian methods. It consists in considering the Bayes factor as a random variable and calculates its distribution, that results from values computed in a frequentist approach after perturbing the data following the model considered. We apply this hybrid method to DESI data, comparing the CPL and w models under various prior conditions, including weak and strong priors, and theory-informed priors. We find that, when the traditional bayes factor is considered, that weak priors favor the w model over CPL, while strong priors favor CPL. Additionally, theory-informed priors further enhance the preference for the w model. While when we apply the BF method, the preference for CPL over w is seen in all cases albeit with similar but reduced impact on the p-value from the different prior considerations. We also tried to generalize further, by perturbing as well the covariance matrix following the model considered, and found that, in general, the current data in that case is not stringent enough to disentangle between the two models. Our results demonstrate that varying the Bayes factor as a random variable, providing that the covariance matrix is kept as model independent, provides a robust model comparison, reducing the impact of prior dependence as well as offering quantitative assessment of the preferences of the competing models.(abridged)

Paper Structure

This paper contains 5 sections, 9 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Theoretical formalism and expectations
  3. Implementation methods and datasets
  4. Results
  5. Summary and conclusions

Figures (5)

  • Figure 1: Bayes factor for the $w$ and $w_0w_a$ models evaluated when considering different priors using Planck 2018 CMB geometrical compressed information, Pantheon+ Supernova sample and DESI BAO measurements.
  • Figure 2: Distribution of $B$ histogram bars and kernel smoothed interpolation solid line assuming either model $w_0w_a$ or model $w$ with equal strong or weak prior for both models (see the legend for details). The vertical lines corresponds to the value of $B$ when the data is not perturbed. Settings are the same as Fig. \ref{['fig:Bfix']}
  • Figure 3: Distribution of $B$ histogram bars and kernel smoothed interpolation solid line assuming either model $w_0w_a$ or model $w$ with equal strong for both models but different theory inspired weak priors (see the legend for details). The vertical lines corresponds to the value of $B$ when the data is not perturbed. Settings are the same as Fig. \ref{['fig:Bfix']}
  • Figure 4: Distribution of $B$ histogram bars and kernel smoothed interpolation solid line assuming either model $w_0w_a$ or model $w$ with equal strong or weak prior for both models (see the legend for details) perturbing the data and the their covariance matrices. The vertical lines corresponds to the value of $B$ with fixed data. Settings are the same as Fig. \ref{['fig:Bfix']}
  • Figure 5: Distribution of $B$ histogram bars and kernel smoothed interpolation solid line assuming either model $w_0w_a$ or model $w$ with equal strong for both models but different theory inspired weak priors (see the legend for details) perturbing the data and the their covariance matrices. The vertical lines corresponds to the value of $B$ with fixed data. Settings are the same as Fig. \ref{['fig:Bfix']}