Bayesian methods for fitting Baryon Acoustic Oscillations in the Lyman-$\alpha$ forest

Understand

We study and compare fitting methods for the Lyman-$\alpha$ (Ly$\alpha$) forest 3D correlation function.

• We use the nested sampler PolyChord and the community code picca to perform a Bayesian analysis which we compare with previous frequentist analyses.
• By studying synthetic correlation functions, we find that the frequentist profile likelihood produces results in good agreement with a full Bayesian analysis.
• On the other hand, Maximum Likelihood Estimation with the Gaussian approximation for the uncertainties is inadequate for current data sets.