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arXiv 2104.02728astro-ph.CO
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从光标准塞壬推算哈勃常数的无偏无似然法

Unbiased likelihood-free inference of the Hubble constant from light standard sirens

Francesca Gerardi, Stephen M. Feeney, Justin Alsing

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19 pages, 8 figures, comments welcome
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摘要：

多信使观测双星中子星合并提供了一个有前途的途径解决的哈勃常数（$H_0$）的紧张局势，提供他们的限制是免费的系统，如Malmquist偏差。在传统的贝叶斯框架中，考虑选择效应的可能性需要计算预期的检测数量（或分数）作为描述人口和宇宙学的参数的函数;这是一个潜在的昂贵和/或不准确的过程。然而，这种计算可以通过在从未明确计算可能性的框架中执行推断来完全绕过，而是使用数据的前向模拟来拟合，其中自然包括选择。无可能性推理（LFI）在这里，我们使用密度估计LFI，结合基于神经网络的数据压缩，在给定每个物体的噪声红移、距离和特殊速度估计的情况下，从二元中子星合并的模拟目录中推断出$H_0$。我们证明，LFI产生统计无偏估计的$H_0$的选择效应的存在下，与精度匹配的抽样完整的贝叶斯分层模型。对于由$O(10^4)$群体组成的训练集，边缘化偏差仅使$H_0$的不确定性增加$6\%$。由此产生的LFI框架是适用于整个天体物理学的选择效应的人口水平的推理问题。

英文摘要：

Multi-messenger observations of binary neutron star mergers offer a promising path towards resolution of the Hubble constant ($H_0$) tension, provided their constraints are shown to be free from systematics such as the Malmquist bias. In the traditional Bayesian framework, accounting for selection effects in the likelihood requires calculation of the expected number (or fraction) of detections as a function of the parameters describing the population and cosmology; a potentially costly and/or inaccurate process. This calculation can, however, be bypassed completely by performing the inference in a framework in which the likelihood is never explicitly calculated, but instead fit using forward simulations of the data, which naturally include the selection. This is Likelihood-Free Inference (LFI). Here, we use density-estimation LFI, coupled to neural-network-based data compression, to infer $H_0$ from mock catalogues of binary neutron star mergers, given noisy redshift, distance and peculiar velocity estimates for each object. We demonstrate that LFI yields statistically unbiased estimates of $H_0$ in the presence of selection effects, with precision matching that of sampling the full Bayesian hierarchical model. Marginalizing over the bias increases the $H_0$ uncertainty by only $6\%$ for training sets consisting of $O(10^4)$ populations. The resulting LFI framework is applicable to population-level inference problems with selection effects across astrophysics.

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