距离阶梯的微妙统计：关于距离先验和选择效应
The subtle statistics of the distance ladder: On the distance prior and selection effects
AI总结：
本文指出距离阶梯分析中常被忽视的两个统计问题：均匀距离模量先验导致距离偏低、哈勃常数偏高，以及选择效应引入额外后验因子；通过解析和模拟量化了这些效应在CosmicFlows-4和SH0ES样本中的影响。
摘要：
统计方法在距离阶梯研究中很少被视为重要因素，或是哈勃张力的潜在贡献者。我们认为应该如此，并强调两个值得注意的问题。首先，天文距离是推断的潜在参数，需要先验。我们表明，贝叶斯距离阶梯分析中常见的（通常是隐式的）距离模量均匀先验，由于物体在体积中均匀分布，会导致距离偏低，从而使哈勃常数偏高。对于体积或红移限制样本，仅当红移不确定性（包括本动速度）消失时，频率学派$\chi^2$方法才是无偏的，尽管基于模拟的校准可以纠正偏差。其次，在贝叶斯框架中，选择效应引入了额外的后验因子，描述了物体在模型下进入样本的概率。这些因子部分抵消了体积先验，具体取决于选择的性质。经过详细的解析和基于模拟的研究，我们量化了CosmicFlows-4和SH0ES样本中的体积先验效应。两者都使用频率学派方法，因此该效应表现为潜在的估计量偏差，而非缺失的先验。隐含的哈勃常数偏移是显著的，但不能天真地应用——还需要原则性的选择建模，正如我们对CosmicFlows-4明确研究的那样。这两种效应应该已经被SH0ES流程中基于模拟的偏差校正所捕获。我们的工作强调了准确建模距离和选择的迫切需要，要么直接在贝叶斯前向模型中，要么通过事后基于模拟的校正，并配合真实的源和选择分布。这种建模需要具有已知、均匀选择标准的样本，未来的巡天应优先考虑这一点。
英文摘要：
Statistical methodology is rarely considered significant in distance-ladder studies or a potential contributor to the Hubble tension. We suggest it should be, highlighting two appreciable issues. First, astronomical distances are inferred latent parameters, requiring a prior. We show that the (often implicit) uniform priors on distance moduli common to Bayesian distance-ladder analyses bias distances low due to objects being uniformly distributed in volume, which biases the Hubble constant high. Frequentist $χ^2$ methods are unbiased for volume- or redshift-limited samples only if the redshift uncertainty (including peculiar velocities) vanishes, though simulation-based calibration can correct the bias. Second, in a Bayesian framework, selection effects introduce additional posterior factors describing the probability of objects entering the sample under the model. These partly counteract the volume prior, depending on the nature of the selection. After detailed analytic and mock-based studies, we quantify the volume-prior effect in the CosmicFlows-4 and SH0ES samples. Both use frequentist methods, so the effect appears as a potential estimator bias rather than a missing prior. The implied Hubble constant shifts are significant but must not be applied na\"ıvely -- principled selection modelling is also required, as we investigate explicitly for CosmicFlows-4. Both effects should already be captured by the SH0ES pipeline's simulation-based bias corrections. Our work highlights the crucial need to model both distances and selection accurately, either directly in a Bayesian forward model, or via post-hoc simulation-based corrections with realistic source and selection distributions. Such modelling requires samples with known, homogeneous selection criteria, which future surveys should prioritise.
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