Unbiased likelihood-free inference of the Hubble constant from light standard sirens,Physical Review D

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Unbiased likelihood-free inference of the Hubble constant from light standard sirens
Physical Review D ( IF 4.6 ) Pub Date : 2021-10-22 , DOI: 10.1103/physrevd.104.083531
Francesca Gerardi ₁ , Stephen M. Feeney ₁ , Justin Alsing _{2,

3}

Affiliation

Multimessenger observations of binary neutron star mergers offer a promising path toward 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.

中文翻译：

从光标准警报器对哈勃常数的无偏似然推断

对双中子星合并的多信使观测为解决哈勃常数提供了一条有希望的途径。

H_{0}

) 张力，前提是它们的约束被证明不受系统性影响，例如 Malmquist 偏差。在传统的贝叶斯框架中，考虑可能性中的选择效应需要计算作为描述种群和宇宙学参数的函数的预期检测数量（或分数）；一个潜在的昂贵和/或不准确的过程。但是，可以通过在从未明确计算似然性而是使用数据的前向模拟（自然包括选择）进行拟合的框架中执行推理来完全绕过此计算。这是无似然推理（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，来推断