BeyondPlanck IV. 论 CMB 分析中的端到端模拟——贝叶斯统计与频率派统计
BeyondPlanck IV. On end-to-end simulations in CMB analysis -- Bayesian versus frequentist statistics
AI总结：
本文探讨了CMB分析中端到端模拟的输入定义问题，区分了贝叶斯模拟与频率派模拟，指出二者在不确定性量化上互补，并利用频率派模拟验证了BeyondPlanck的核心底层算法。
摘要：
端到端模拟在任何高灵敏度 CMB 实验的分析中发挥着关键作用，提供了任何其他方法都无法比拟的高保真系统误差传播能力。在本文中，我们探讨了关于此类模拟的一个重要问题，即如何根据天空模型和仪器参数来定义输入。这些输入既可以作为从数据导出的约束实现，也可以作为独立于数据的随机实现。我们将这两种方式分别称为贝叶斯模拟和频率派模拟。我们表明，这两种选择会导致显著不同的相关结构，因为频率派模拟与贝叶斯模拟相反，有效地包含了宇宙方差，但排除了来自非线性简并的特定实现相关性。因此，它们量化了根本不同类型的不确定性，我们认为它们因此也具有不同且互补的科学用途，即使这种二分法并非绝对。在 BeyondPlanck 之前，大多数流程都混合使用约束输入和随机输入，并将相同的混合模拟用于所有应用，尽管其统计依据并不总是显而易见的。BeyondPlanck 代表了第一个能够生成这两种类型模拟的端到端 CMB 模拟框架，这些新功能使该主题成为焦点。贝叶斯 BeyondPlanck 模拟及其用途在一系列配套论文中进行了广泛描述。在本文中，我们考虑了相应的频率派模拟的一个重要应用，即代码验证。也就是说，我们生成了一组具有已知输入的 1 年 LFI 30 GHz 频率派模拟，并使用它们来验证 BeyondPlanck 的核心底层算法；增益估计、相关噪声估计和地图制作。
英文摘要：
End-to-end simulations play a key role in the analysis of any high-sensitivity CMB experiment, providing high-fidelity systematic error propagation capabilities unmatched by any other means. In this paper, we address an important issue regarding such simulations, namely how to define the inputs in terms of sky model and instrument parameters. These may either be taken as a constrained realization derived from the data, or as a random realization independent from the data. We refer to these as Bayesian and frequentist simulations, respectively. We show that the two options lead to significantly different correlation structures, as frequentist simulations, contrary to Bayesian simulations, effectively include cosmic variance, but exclude realization-specific correlations from non-linear degeneracies. Consequently, they quantify fundamentally different types of uncertainties, and we argue that they therefore also have different and complementary scientific uses, even if this dichotomy is not absolute. Before BeyondPlanck, most pipelines have used a mix of constrained and random inputs, and used the same hybrid simulations for all applications, even though the statistical justification for this is not always evident. BeyondPlanck represents the first end-to-end CMB simulation framework that is able to generate both types of simulations, and these new capabilities have brought this topic to the forefront. The Bayesian BeyondPlanck simulations and their uses are described extensively in a suite of companion papers. In this paper we consider one important applications of the corresponding frequentist simulations, namely code validation. That is, we generate a set of 1-year LFI 30 GHz frequentist simulations with known inputs, and use these to validate the core low-level BeyondPlanck algorithms; gain estimation, correlated noise estimation, and mapmaking.
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