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Despite increasingly precise observations and sophisticated theoreticalmodels, the discrepancy between measurements of H0 from the cosmic microwavebackground or from Baryon Acoustic Oscillations combined with Big-BangNucleosynthesis versus those from local distance ladder probes -- commonlyknown as the $H_0$ tension -- continues to perplex the scientific community. Toaddress this tension, Early Dark Energy (EDE) models have been proposed asalternatives to $\Lambda$CDM, as they can change the observed sound horizon andthe inferred Hubble constant from measurements based on this. In this paper, weinvestigate the use of Bayesian Model Averaging (BMA) to evaluate EDE as asolution to the H0 tension. BMA consists of assigning a prior to the model andderiving a posterior as for any other unknown parameter in a Bayesian analysis.BMA can be computationally challenging in that one must approximate the jointposterior of both model and parameters. Here we present a computationalstrategy for BMA that exploits existing MCMC software and combinesmodel-specific posteriors post-hoc. In application to a comprehensive analysisof cosmological datasets, we quantify the impact of EDE on the H0 discrepancy.We find an EDE model probability of $\sim$90% whenever we include the H0measurement from Type Ia Supernovae in the analysis, whereas the other datashow a strong preference for the standard cosmological model. We finallypresent constraints on common parameters marginalized over both cosmologicalmodels. For reasonable priors on models with and without EDE, the H0 tension isreduced by at least 20%.

A convenient approach to characterizing model uncertainty with application to early dark energy solutions of the Hubble tension