Statistical properties and probability densities of correlation functions

相关函数的统计特性和概率密度

• 批准号: 178182033
• 负责人: Professor Dr. Peter Schneider
• 金额: --
• 依托单位: Argelander-Institut für Astronomie
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2010
• 资助国家: 德国
• 起止时间: 2009-12-31 至 2014-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/178182033?language=en
• 关键词: Statistical; properties; probability; densities; correlation

In a recent publication (Schneider & Hartlap 2009), we discovered that correlation functions of statistical processes have to obey a set of inequalities and that, as a consequence, the probability density of measured correlation functions cannot be a multi-variate Gaussian, as almost always assumed when comparing observations with model predictions to obtain parameter estimates. As we could demonstrate, this effect is severe and affects the results of the analysis of at least some recent cosmological surveys – in those cases, the Gaussian is not even a reasonable approximation. The goal of this project is to obtain an approximate description of the probability density of correlation functions without violation of the strict inequalities, needed not only for precision cosmology. Based on the aforementioned paper and two ongoing diploma theses, a combination of analytical and numerical methods will be employed to derive approximations for this probability density which obey all the necessary inequalities and to generalize this probability to other second-order statistical measures of a random process (such as the cosmological density field). The resulting densities will then be applied to the analysis of several mock and possibly real cosmological surveys, using Maximum Likelihood and Bayesian methods.

在最近的出版物（Schneider & Hartlap 2009）中，我们发现统计过程的相关函数必须服从一组不等式，因此，测量的相关函数的概率密度不可能是多变量高斯分布，因为在将观测与模型预测进行比较以获得参数估计时几乎总是假设。正如我们可以证明的那样，这种效应是严重的，至少影响了最近一些宇宙学调查的分析结果-在这些情况下，高斯甚至不是一个合理的近似。这个项目的目标是获得一个近似描述的概率密度的相关函数，而不违反严格的不等式，需要不仅是精确的宇宙学。基于上述文件和两个正在进行的文凭论文，分析和数值方法的组合将被用来获得近似这个概率密度服从所有必要的不等式和推广这个概率到其他二阶统计措施的随机过程（如宇宙密度场）。然后，使用最大似然法和贝叶斯法，将所得密度应用于分析几个模拟和可能的真实的宇宙学调查。

项目成果

Constrained correlation functions from the Millennium Simulation

千年模拟中的约束相关函数

• DOI: 10.1051/0004-6361/201525906
• 发表时间: 2015
• 期刊: arXiv: Cosmology and Nongalactic Astrophysics
• 作者: Wilking;Röseler;Schneider
• 通讯作者: Schneider

The bispectrum covariance beyond Gaussianity - A log-normal approach

超越高斯性的双谱协方差 - 对数正态方法

• DOI: 10.1051/0004-6361/201118020
• 发表时间: 2012
• 期刊: Astronomy and Astrophysics
• 影响因子: 6.5
• 作者: Martin;Schneider
• 通讯作者: Schneider

A quasi-Gaussian approximation for the probability distribution of correlation functions

相关函数概率分布的拟高斯近似

• DOI: 10.1051/0004-6361/201321718
• 发表时间: 2013
• 期刊: Astronomy and Astrophysics
• 影响因子: 6.5
• 作者: Wilking;Schneider
• 通讯作者: Schneider