We present a Bayesian hierarchical framework for a principled data analysis pipeline of peculiar velocity surveys, which makes explicit the inference problem of constraining cosmological parameters from redshift-independent distance indicators. We demonstrate our method for a Fundamental Plane-based survey. The essence of our approach is to work closely with observables (e.g. angular size, surface brightness, redshift, etc), through which we bypass the use of summary statistics by working with the probability distributions. The hierarchical approach improves upon the usual analysis in several ways. In particular, it allows a consistent analysis without having to make prior assumptions about cosmology during the calibration phase. Moreover, calibration uncertainties are correctly accounted for in parameter estimation. Results are presented for a new, fully analytic posterior marginalised over all latent variables, which we expect to allow for more principled analyses in upcoming surveys. A maximum a posteriori estimator is also given for peculiar velocities derived from Fundamental Plane data.

中文翻译：

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特殊速度的宇宙学推断的概率框架

我们为特殊速度调查的原则性数据分析管道提出了贝叶斯分层框架，这明确了从红移独立距离指标约束宇宙学参数的推理问题。我们展示了我们的基于基本平面的调查方法。我们方法的本质是与可观测值（例如角大小、表面亮度、红移等）密切合作，通过使用概率分布，我们绕过了汇总统计的使用。分层方法在几个方面改进了通常的分析。特别是，它允许进行一致的分析，而无需在校准阶段对宇宙学做出事先假设。此外，在参数估计中正确考虑了校准不确定性。结果是针对所有潜在变量的新的、完全分析的后验边缘化的，我们希望在即将进行的调查中进行更原则性的分析。还给出了从基面数据导出的特殊速度的最大后验估计量。