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arXiv 1504.03979astro-ph.CO
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从星系团推断宇宙学参数:功率谱后验分布的影响

Cosmological parameter inference from galaxy clustering: The effect of the posterior distribution of the power spectrum

Benedict Bahr-Kalus, Will J. Percival, Lado Samushia

摘要:

我们认为后验分布的形状时,使用拟合宇宙学模型测量星系调查的功率谱。在非常大的尺度上,幂中的高斯后验分布不近似于我们对高斯密度场$δ_k$期望的后验分布$\mathcal{P}_R$,即使我们根据待测模型改变协方差矩阵。我们比较替代后验分布与$\mathcal{P}_R$,无论是模式的模式和预期的测量原始非高斯参数化的$f_\mathrm{NL}$。在协方差矩阵固定的高斯后验分布$\mathcal{P}_f$上进行边缘化,得到$f_\mathrm{NL}$的后验均值,对于具有欧几里得特征的数据集,$\triangle f_\mathrm{NL}=0.4$会低估$f_\mathrm{NL}$的后验均值,而对于斯隆数字巡天(SDSS)-III重子振荡光谱巡天(BOSS)的数据发布9(DR 9),$\triangle f_\mathrm{NL}=19.1$会低估$f_\mathrm{NL}$的后验均值。采用不同形式的后验函数意味着我们不一定需要每个待检验模型的不同协方差矩阵:这种依赖性被吸收到后验函数的函数形式中。因此,分析的计算负担显著降低。

英文摘要:

We consider the shape of the posterior distribution to be used when fitting cosmological models to power spectra measured from galaxy surveys. At very large scales, Gaussian posterior distributions in the power do not approximate the posterior distribution $\mathcal{P}_R$ we expect for a Gaussian density field $δ_k$, even if we vary the covariance matrix according to the model to be tested. We compare alternative posterior distributions with $\mathcal{P}_R$, both mode-by-mode and in terms of expected measurements of primordial non-Gaussianity parameterised by $f_\mathrm{NL}$. Marginalising over a Gaussian posterior distribution $\mathcal{P}_f$ with fixed covariance matrix yields a posterior mean value of $f_\mathrm{NL}$ which, for a data set with the characteristics of Euclid, will be underestimated by $\triangle f_\mathrm{NL}=0.4$, while for the data release 9 (DR9) of the Sloan Digital Sky Survey (SDSS)-III Baryon Oscillation Spectroscopic Survey (BOSS) it will be underestimated by $\triangle f_\mathrm{NL}=19.1$. Adopting a different form of the posterior function means that we do not necessarily require a different covariance matrix for each model to be tested: this dependence is absorbed into the functional form of the posterior. Thus, the computational burden of analysis is significantly reduced.

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