We investigate the impact of each ingredient in the employed physical data model on the Bayesian forward inference of initial conditions from biased tracers at the field level. Specifically, we use dark matter halos in a given cosmological simulation volume as tracers of the underlying matter density field. We study the effect of tracer density, grid resolution, gravity model, bias model and likelihood on the inferred initial conditions. We find that the cross-correlation coefficient between true and inferred phases reacts weakly to all ingredients above, and is well predicted by the theoretical expectation derived from a Gaussian model on a broad range of scales. The bias in the amplitude of the inferred initial conditions, on the other hand, depends strongly on the bias model and the likelihood. We conclude that the bias model and likelihood hold the key to an unbiased cosmological inference. Together they must keep the systematics — which arise from the sub-grid physics that are marginalized over — under control in order to obtain an unbiased inference.

我们研究了所采用的物理数据模型中的每种成分对来自现场级别的有偏示踪剂的初始条件的贝叶斯前向推断的影响。具体来说，我们在给定的宇宙学模拟体积中使用暗物质晕作为底层物质密度场的示踪剂。我们研究了示踪剂密度、网格分辨率、重力模型、偏差模型和可能性对推断的初始条件的影响。我们发现真实相和推断相之间的互相关系数对上述所有成分的反应都很弱，并且可以通过从高斯模型在广泛的尺度上得出的理论期望得到很好的预测。另一方面，推断的初始条件的幅度偏差在很大程度上取决于偏差模型和可能性。我们得出结论，偏差模型和可能性是无偏宇宙学推断的关键。他们必须一起控制系统学——从被边缘化的亚网格物理学中产生——以获得无偏见的推论。