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. We compute for the first time the full posterior distribution from the Ly$\alpha$ forest correlation functions measured by the extended Baryon Oscillation Spectroscopic Survey (eBOSS). We highlight the benefits of sampling the full posterior distribution by expanding the baseline analysis to better understand the contamination by Damped Ly$\alpha$ systems (DLAs). We make our improvements and results publicly available as part of the picca package.

中文翻译：

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在 Lyman-α 森林中拟合重子声学振荡的贝叶斯方法

我们研究并比较了 Lyman-$\alpha$ (Ly$\alpha$) 森林 3D 相关函数的拟合方法。我们使用嵌套采样器 PolyChord 和社区代码 picca 来执行贝叶斯分析，并将其与之前的频率分析进行比较。通过研究综合相关函数，我们发现频率论者轮廓似然产生的结果与完整的贝叶斯分析非常吻合。另一方面，不确定性的高斯近似的最大似然估计对于当前数据集是不够的。我们第一次计算了由扩展重子振荡光谱测量 (eBOSS) 测量的 Ly$\alpha$ 森林相关函数的完整后验分布。我们通过扩展基线分析来强调对完整后验分布进行采样的好处，以更好地了解阻尼 Ly$\alpha$ 系统（DLA）的污染。我们将我们的改进和结果作为 picca 包的一部分公开。