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arXiv 2103.04158astro-ph.COastro-ph.IMstat.AP
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宇宙学中关联函数和场级推论的准确度和精密度

On the accuracy and precision of correlation functions and field-level inference in cosmology

Florent Leclercq, Alan Heavens

摘要:

本文对宇宙学数据分析中的关联函数方法和全场推断方法的准确度和精度进行了比较研究。为此,我们研究了贝叶斯分层模型,预测对数正态字段和他们的两点关联函数。虽然对数正态模型是一个简化的解析模型,但它产生的场与现今的非高斯宇宙学密度场具有许多共同的基本特征。我们使用三种不同的统计技术:(一)一个标准的似然为基础的分析的两点关联函数;(二)似然免费(模拟为基础的)分析的两点关联函数;(三)场一级的分析,可能通过更复杂的数据同化技术。我们发现,(a)标准的假设,写下一个可能性的关联函数可能会导致显着的偏见,一个问题是缓解与基于模拟的推理;和(b)分析整个领域提供了相当大的优势,通过更高的准确性,更高的精度,或两者兼而有之的关联函数。增益取决于非高斯性的程度,但在所有情况下,包括弱非高斯性,分析全场的优势是巨大的。

英文摘要:

We present a comparative study of the accuracy and precision of correlation function methods and full-field inference in cosmological data analysis. To do so, we examine a Bayesian hierarchical model that predicts log-normal fields and their two-point correlation function. Although a simplified analytic model, the log-normal model produces fields that share many of the essential characteristics of the present-day non-Gaussian cosmological density fields. We use three different statistical techniques: (i) a standard likelihood-based analysis of the two-point correlation function; (ii) a likelihood-free (simulation-based) analysis of the two-point correlation function; (iii) a field-level analysis, made possible by the more sophisticated data assimilation technique. We find that (a) standard assumptions made to write down a likelihood for correlation functions can cause significant biases, a problem that is alleviated with simulation-based inference; and (b) analysing the entire field offers considerable advantages over correlation functions, through higher accuracy, higher precision, or both. The gains depend on the degree of non-Gaussianity, but in all cases, including for weak non-Gaussianity, the advantage of analysing the full field is substantial.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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